Browse Rational problems Studdy Solved!

Problem 1101

When algebraic fractions are combined, sometimes the answer needs to be factored in order to reduce it to lowest terms. $\frac{x^2}{x-y} - \frac{y^2}{x-y} = \frac{x^2 - y^2}{x-y} = \frac{(x+y)(x-y)}{(x-y)} = x+y$ $\frac{5a+3b}{2} + \frac{a-b}{2} = \frac{5a+3b+a-b}{2} = \frac{6a+2b}{2} = \frac{2(3a+b)}{2} = 3a+b$
Combine the following. The answers will need to be factored in order to reduce them to lowest terms.
18. $\frac{a^2}{a+b} - \frac{b^2}{a+b} =$
19. $\frac{8a-4y}{3} - \frac{2a+2y}{3} =$
20. $\frac{9x+2y}{4} - \frac{x-2y}{4} =$
21. $\frac{4x}{x+2y} + \frac{8y}{x+2y} =$
22. $\frac{2x-y}{4} + \frac{2x+5y}{4} =$

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Problem 1102

$\frac{x+5}{x} + \frac{7}{x(x+8)} =$

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Problem 1103

Analyzing and graphing rational functions.pdf Download Analyzing and graphing rational functions.pdf (414 KB) Page 8
4. $f(x)=\frac{2 x^{2}}{x^{2}-1}$

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Problem 1104

$\frac{\text { 所 }}{36}=\frac{8}{9}$

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Problem 1105

Evaluate the expression for the given variable value. $2r = \frac{3}{4}$ ; $r = \frac{3}{2}$ (Type a whole number, fraction, or mixed number.)

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Problem 1106

$-\frac{5}{9}(k+2)=-2$
Write your answer as a fraction $k=$

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Problem 1107

$M_1V_1 = M_2V_2$
where $M_1$ and $V_1$ are the concentration and volume of the concentrated solution and $M_2$ and $V_2$ are the concentration and volume of the dilute solution.
Rearrange the equation to solve for $M_1$ .
$M_1 = \frac{M_2V_2}{V_1}$
A chemist prepares 350.0 mL of a 0.589 M solution using 35.0 mL of a more concentrated solution. What is the concentration ( $M_1$ ) of the more concentrated solution?
$M_1 =$ _______ M

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Problem 1108

20. A student walks 3 km to school in 40 minutes and then runs 3 km back in 20 minutes. What is their average velocity for the round trip?

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Problem 1109

Find the holes of the function $f(x) = \frac{(x+4)(x-2)}{(x-5)(x-2)}$ .

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Problem 1110

Solve each inequality.
7) $\frac{10}{x-5} \ge \frac{11}{x-6}$
8) $-\frac{3}{x+7} \le -\frac{4}{x+8}$
9) $-\frac{7}{x+5} \le -\frac{8}{x+6}$
10) $\frac{(x+7)(x-3)}{(x-5)^2} > 0$

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Problem 1111

$f(x) = \frac{7x}{x-4}$
The equation(s) of the vertical asymptote(s) is/are $x = 4$ .
The equation(s) of the horizontal asymptote(s) is/are $y = 7$ .
$f(x) = \frac{7x}{x-4}$

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Problem 1112

Solve for x using cross multiplication. $\begin{array}{c} \frac{x-3}{2}=\frac{x-4}{3} \\ x=[?] \end{array}$ Enter

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Problem 1113

Let $f(x)=\frac{3 x^{2}+11 x-4}{2 x^{2}-5 x+2}$ This function has: 1) $A y$ intercept at the point $\square$ 2) $x$ intercepts at the point(s) $\square$ 3) Vertical asymptotes at $x=$ $\square$ 4) Horizontal asymptote at $y=$ $\square$

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Problem 1114

MATH-1314-61408-College Algebra nework: Practice Final Exam - Homework Question 2,
Find the domain of the function. $f(x)=\frac{x+7}{6-x}$

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Problem 1115

Solve the following equation for $q$ :
$\frac{10}{q-7} = \frac{6}{q}$
$q =$
Help: If there is more than one correct answer, enter your answers as a comma separated list. If the equation has no real solution, write "No Solution."

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Problem 1116

Perform the operation and simplify the result when possible. $\frac{x}{x^2 + 5x + 6} + \frac{x}{x^2 - 4}$ Submit Answer

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Problem 1117

Perform the division. $\frac{7x^7y^6 + 14x^5y - 21xy^7}{-7x^6y^6}$ $-x - \frac{2}{xy^5} + \frac{3y}{x^6}$ $-x - \frac{2}{xy^6} + \frac{3y}{x^5}$ $-x - \frac{2}{xy^5} - \frac{3y}{x^5}$ $x + \frac{2}{xy^5} - \frac{3y}{x^5}$ $-x - \frac{2}{xy^5} + \frac{3y}{x^5}$ Submit Answer

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Problem 1118

4. Mary and Joe can complete a job together in 6 hours. Mary can do the job in 14 hours working alone. How long would it take Joe to complete the job if he is working alone?

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Problem 1119

Simplify. $\frac{6u^3 w^4}{2u^3 v^2 + 10u}$

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Problem 1120

$f(x) = \frac{3x+3}{x+2}$
Graph the rational function.
Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.

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Problem 1121

65) $f(x) = \frac{x^2 - 6x + 2}{x+8}$
A) $x = y + 6$ B) $y = x - 14$ Objective: (4.5) Find Oblique Asymptote of Rational Function
Solve.
66) $x^2 - 9x + 20 > 0$
A) $(5, \infty)$ B) $(-\infty, 4) \cup (5, \infty)$ Objective: (4.6) Solve Quadratic Polynomial Inequality
List the critical values of the related function. Then solve the inequality.
67) $\frac{1}{x+6} > 0$
A) No critical values; $\emptyset$ B) $-6; (-\infty, -6)$ Objective: (4.6) Solve Rational Inequality I

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Problem 1122

a) $\frac{7}{q-2} \cdot \frac{2 q-4}{q+4}$

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Problem 1123

$f(x) = \frac{x^2 - 1}{-x^3 - x^2}$
If there is more than one answer, enter your answers as a comma separated list. If there is no solution, enter NONE. Do not leave a blank empty.
(a) The function has x-intercept(s) at $x =$
(b) The function has y-intercept(s) at $y =$
(c) The function has vertical asymptote(s) when $x =$
(d) The function has horizontal asymptote(s) when $y =$
Note: You can earn partial credit on this problem.

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Problem 1124

Simplify: $\frac{x^{2}-x-12}{9-x} \div \frac{x+3}{x+4}$
0:00
Select one: a. $\frac{x^{2}-16}{9-x}$ b. $9-x$ c. $\frac{-x^{2}-6 x+9}{9-x}$ d. $\frac{9-x}{x^{2}-16}$

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Problem 1125

(c) $14m \div (-2m)=$

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Problem 1126

lomework: Practice Final Exam - Homework Question $32,4.5 .27$ lode stion list question 31
Question 32
Question 33
Determine the oblique asymptote of the graph of the function. $g(x)=\frac{x^{2}+5 x-2}{x+3}$
The equation of the oblique asymptote is $\square$ .

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Problem 1127

Solve the formula $N=\frac{U P}{U+9}$ for the variable $P$ . $P=$

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Problem 1128

Find the partial fraction decomposition for the rational expression. $\frac{-31x - 85}{2x^2 + 13x + 20}$

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Problem 1129

(b) $\frac{3b+2}{7b-2} - \frac{3b+2}{2-7b}$
14. Simplify.
(a) $\frac{4}{x^2 - 3x} + \frac{x}{x^2 + 2x - 15}$
(b) $\frac{x}{x^2 - 4} - \frac{3}{x^2 - 2x}$
15. Simplify

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Problem 1130

Find the vertical asymptote(s) of the graph of the function.
$f(x) = \frac{2-x}{(x-3)(x+5)}$
This question: 1 point(s) possible
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one vertical asymptote $\boxed{}$ (Type an equation.)
B. The function has two vertical asymptotes. The leftmost asymptote is $\boxed{}$ and the rightmost asymptote is $\boxed{}$ (Type equations.)
C. The function has no vertical asymptotes.

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Problem 1131

$f(x) = \frac{|x - 5| \cdot x}{x(x^2 + 14x - 95)}$

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Problem 1132

Extra credit 2: Let $r(x) = \frac{(x+3)(x-2)^2}{(x-1)^4}$
a) Are there any holes? If so, where are they?
b) What are the intercepts of $r(x)$ ? x-intercepts: y-intercept:
c) What is/are the vertical asymptote(s) of $r(x)$ ?
d) What is the horizontal asymptote of $r(x)$ ?
e) Use parts a-d to sketch the graph of $r(x)$ below.

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Problem 1133

Find "a" and "b" so that the equation produces the graph below. $\begin{array}{l} y=\frac{a x}{x+b} \\ a=\square \\ b=\square \end{array}$

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Problem 1134

Simplify the product $\frac{w}{12w + 2w^2} \times \frac{9w^3 + 54w^2}{6w^2 - 6w}, w = -6, 0, 1.$ The answer is
Select one: a. $\frac{3w}{4(w-1)}$ b. $\frac{3}{4(w-1)}$ c. $\frac{3w}{4(w+1)}$ d. $\frac{3}{4(w+1)}$

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Problem 1135

$-\frac{1}{3}(x+y) + \frac{2}{3}(x+y)$

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Problem 1136

$-\frac{1}{3}(x+y) + \frac{2}{3}(x+y)$

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Problem 1137

Divide. $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}$ $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}=$ $\square$ (Simplify your answer.)

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Problem 1138

Simplify:? $\left(\frac{2x^2 + 5x + 2}{x + 1}\right)\left(\frac{x^2 - 1}{x + 2}\right)$

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Problem 1139

Add. The numerator should be expanded and simplified. The denominator should be either expanded or factored. $\frac{2}{x-4} + \frac{9}{x+3} =$

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Problem 1140

Simplify the expression. $\frac{4 x-4}{3 x-15}$
Select the correct choice below and fill in any A. $\frac{4 x-4}{3 x-15}=$ $\square$ B. The expression cannot be simplified.

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Problem 1141

Question 19 of 42 Step 2 of 2 01:58:46
Consider the following equation: $\frac{-2 x}{x+1}=-2+\frac{1}{x+3}$
Step 2 of 2: Solve the equation, if possible. If there is a solution, express your answer as either an integer or a simplified fraction.
AnswerHow to enter your answer (opens in new window) 2 Points Keypad Keyboard Shortcuts
Separate your answers with commas, if necessary. Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. Next

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Problem 1142

$H_3 / (G_3 * G_4 * (1 + G_3 * G_4 * H_2))$

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Problem 1143

$y=\frac{6-x}{-x^{3}-9}$

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Problem 1144

$f(x) = \frac{2x^2 + 2x}{x^2 - 2x - 3}$ What are the coordinates of the hole, if one exists. (-1, -2) (-1, $\frac{1}{2}$ ) there isn't one (-1, $-\frac{1}{2}$ )

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Problem 1145

Find the partial fraction decomposition of $\frac{-53x + 54}{12x^2 - 23x + 10}$ .
To set it up first write in the form $\frac{A}{3x - 2} + \frac{B}{4x - 5}$
$\frac{-53x + 54}{12x^2 - 23x + 10} = \frac{\text{ }}{\text{ }} + \frac{\text{ }}{\text{ }}$
Next Question

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Problem 1146

Solve each equation. Remember to check for extraneous solutions.
11) $\frac{a-6}{6a^2} = \frac{1}{6a^2} + \frac{a+5}{3a^2}$

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Problem 1147

4. What value of $r$ makes this equation true? $336 \div r=48$ a. 7 b. 6 c. 8 d. 9

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Problem 1148

What is the sum of the rational expressions below? $\frac{2x+3}{3x} + \frac{x}{x+1}$
A. $\frac{3x^2+2x+4}{4x+1}$ B. $\frac{3x+3}{4x+1}$ C. $\frac{2x^2+3x}{3x^2+3x}$ D. $\frac{5x^2+5x+3}{3x^2+3x}$

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Problem 1149

2) $\frac{7x^2 + 35x}{x + 5}$

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Problem 1150

Solve for $v$ .
$\frac{4}{5v - 20} - 3 = -\frac{8}{v - 4}$
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

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Problem 1151

$S + \frac{17}{6} = \frac{57}{7}$

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Problem 1152

Add. $\frac{7}{4x} + \frac{x-5}{6x^2}$
Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
A. $\frac{7}{4x} + \frac{x-5}{6x^2} =$ $\quad$ , $x \ne$ $\quad$ B. $\frac{7}{4x} + \frac{x-5}{6x^2} =$ $\quad$ , no numbers must be excluded.

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Problem 1153

1) Evaluate $\frac{2}{5}k - 3.5$ for $k = 15$ .

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Problem 1154

1 Find the slant asymptote of the function $f(x)=\frac{x^{2}+4 x-8}{x+3}$ ?

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Problem 1155

Write the form of the partial fraction decomposition of the rational expression given below. Do not solve for the constants. $\frac{x-5}{x^2 + 9x + 18}$

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Problem 1156

Find the vertical asymptotes. $g(r)=\frac{r-7}{r^{2}-2 r-8}$
Enter your answers in increasing order. $\begin{array}{l} r= \\ r= \end{array}$

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Problem 1157

Consider the following rational function. $f(x) = \frac{-2}{x-5}$ Step 1 of 3: Find equations for the vertical asymptotes, if any, for the function. Answer (opens in new window) 2 Points Separate multiple equations with a comma. Selecting a button will replace the entered answer value. The value of the button is used instead of the value in the none

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Problem 1158

Which values are NOT in the domain of the rational function? $f(x) = \frac{(x - 1)(x + 2)}{x^2 - 9}$

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Problem 1159

Identify the vertical asymptote(s) of the rational function. $f(x) = \frac{x(x+6)(x-10)}{(x-5)(x+6)}$

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Problem 1160

Question 5 The partial fraction decomposition of $\frac{x^{2}+12}{(x-3)\left(x^{2}+4\right)}$ can be written in the form of $\frac{f(x)}{x-3}+\frac{g(x)}{x^{2}+4}$ . The possible anwsers for $f(x)$ and $g(x)$ are (a) $A$ , a constant, or (b) $A x+B$ , a linear function. $f(x)$ is in the form of (input a or b) $\square$ and $g(x)$ is in the form of (input a or b ) $\square$

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Problem 1161

(d) $\frac{x^2 - 3x + 2}{x^3 + 4x} \le 0$
When does the graph of $\frac{x^2 + 2x - 4}{x(x-2)^2}$ lie above the graph of $\frac{2}{x(x-2)}$ ?
3. Logarithmic Functions

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Problem 1162

30. Solve: $\frac{x+3}{x^{2}+5 x+6}=\frac{3}{2 x+4}-\frac{1}{x+3}$

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Problem 1163

Solve for $h$ in the literal equation: $A = \frac{1}{2}(b_1 + b_2)h$
$h = 2A(b_1 + b_2)$
$h = \frac{b_1 + b_2}{2A}$
$h = \frac{2A}{b_1 + b_2}$
$h = \frac{A}{2(b_1 + b_2)}$

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Problem 1164

What mass of NaCl are dissolved in 152 mL of a solution if the concentration of the solution is $0.364$ M? $3.24$ g of NaCl will be required

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Problem 1165

kam Question 12 of 22
This test: 22 point(s) possible This question: 1 point(s) possible Submit test
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 4 hours, while the outlet pipe can empty it in 10 hours. How long will it take to fill the vat if both pipes are left open?
It will take $\square$ hours. (Simplify yournanswer. Do not round.)

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Problem 1166

Add and simplify: $\frac{2}{x+9} + \frac{x+45}{x^2 - 81}$

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Problem 1167

$\mathrm{A} = \frac{\mathrm{r}}{2 \mathrm{~L}}$ Solve for $L$ .

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Problem 1168

Simplify the complex rational expression using either Method I or Method II. $\frac{\frac{y}{2} - \frac{2}{y}}{\frac{2}{y^2} - \frac{1}{2}} = \text{?}$

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Problem 1169

The partial fraction decomposition of $\frac{-5 x^{2}+31 x+8}{(x-3)\left(x^{2}+3 x+10\right)}$ can be written in the form of $\frac{f(x)}{(x-3)}+\frac{g(x)}{\left(x^{2}+3 x+10\right)}$ , where $\begin{array}{l} f(x)=\square \\ g(x)=\square \end{array}$

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Problem 1170

Select the expression from the options below that properly sets up the partial fraction decomposition for the following rational expression: $\frac{x^{3}+15}{x(x-3)^{2}\left(x^{2}+2\right)^{3}}$
Select the correct answer below: $\frac{A}{x}+\frac{B}{x-3}+\frac{C}{x^{2}+2}$ $\frac{A}{x}+\frac{B}{x-3}+\frac{C}{x+2}+\frac{D}{x^{2}+2}+\frac{E}{x^{3}+2}$ $\frac{A}{x}+\frac{B}{x-3}+\frac{C}{x+2}+\frac{D x+E}{x^{2}+2}$ $\frac{A}{x}+\frac{B}{x-3}+\frac{C x+D}{\left(x^{2}+2\right)^{2}}+\frac{E x+F}{\left(x^{2}+2\right)^{3}}$ $\frac{A}{x}+\frac{B}{x-3}+\frac{C x+D}{\left(x^{2}+2\right)}+\frac{E x+F}{\left(x^{2}+2\right)^{2}}+\frac{G x+H}{\left(x^{2}+2\right)^{3}}$ $\frac{A}{x}+\frac{B}{x-3}+\frac{C}{(x-3)^{2}}+\frac{D x+E}{x^{2}+2}+\frac{F x+G}{\left(x^{2}+2\right)^{2}}+\frac{H x+I}{\left(x^{2}+2\right)^{3}}$

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Problem 1171

For the following expression, find the correct partial fraction decomposition for $\frac{3 x^{2}+22 x+1}{(5 x+3)\left(x^{2}-2 x+4\right)}$
Provide your answer below: $\square$ $+$ $\square$

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Problem 1172

Question For the following expression, find the correct partial fraction decomposition. $\frac{-z^{3}-z^{2}+z-5}{\left(z^{2}+2\right)\left(z^{2}+2\right)}$

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Problem 1173

For the following expression, find the correct partial fraction decomposition. $\frac{-3 y^{3}+10 y^{2}-20 y+3}{\left(y^{2}-3 y+5\right)\left(y^{2}-3 y+5\right)}$

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Problem 1174

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. $\frac{x+2}{x+5}<2$ \begin{tabular}{|c|c|c|c|} \hline Interval & $\square$ & $\square$ & $\square$ \\ \hline Sign & $\square$ & $\square$ & $\square$ \\ \hline \end{tabular} (Type your answers in interval notation. Use ascending order.) Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set.
Which number line below shows the graph of the solution set? A. $\qquad$ $B$ c. E.
F

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Problem 1175

Question8: Solve in the set of real numbers the equation: $\frac{x^{2}+5 x-24}{x-5} \leq 0$ , using completing the square method

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Problem 1176

If a certain number is added to the denominator of the fraction $\frac{3}{5}$ and 7 is added to the numerator, the result is a fraction that will reduce to $\frac{1}{2}$ . What number is added to the denominator?
Let $x=$ the number added to the denominator. $\frac{3+7}{5+x}=\frac{1}{2}$

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Problem 1177

Subtract. Simplify the result if possible. $\begin{array}{l} \frac{4 m}{m-3}-\frac{12}{m-3} \\ \frac{4 m}{m-3}-\frac{12}{m-3}= \end{array}$

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Problem 1178

Multiply. $\frac{4 x-16}{6 x^{2}+x} \cdot \frac{6 x^{2}+25 x+4}{x^{2}-16}$ $\frac{4 x-16}{6 x^{2}+x} \cdot \frac{6 x^{2}+25 x+4}{x^{2}-16}=$ $\qquad$ (Type your answer in factored form.)

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Problem 1179

Simplify the complex fraction. $\frac{2 s-\frac{2}{s}}{6+\frac{2}{s}}$
Need Help? Read It Watch It Submit Answer

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Problem 1180

Add, and then simplify, if possible. $\frac{7}{4 y}+\frac{12}{4 y}$ $\square$ Need Help? Read II

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Problem 1181

Find the value of the expression $(66 \div p) \cdot 332$ for $p=33$ .

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Problem 1182

Find the partial fraction decomposition of the following rational expression. $\begin{array}{l} \frac{12}{x\left(x^{2}+4\right)} \\ \frac{12}{x\left(x^{2}+4\right)}= \end{array}$ $\square$ (Use integers or fractions for any numbers in the expression.)

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Problem 1183

DATE:
REVIEW QUESTIONS - PART 4 answer $\qquad$ - Encircle the letter that corresponds to the correct
Rational and Radical Functions
1. Find the value of the expression if $x=9$ $\frac{x^{2}+3}{x+6}$ a. $-84 / 15$ b. $15 / 84$ c. $28 / 5$ d. $-15 / 84$
1. Type the given expression in Desmos Scientific Calculator (not graphing) but
HINT: $\quad 2$ instead of putting $x$ , replace it with parenthesis.
2. Put 9 in the parenthesis and click equals.
3. To convert decimal to fraction, click
2. Find the value of the expression if $\mathrm{x}=-6$ and $\mathrm{y}=1 . \quad \frac{x y^{2}}{-6}$ a. 1
1. Type the given expression in Desmos Scientific Calculator (not graphing) but instead of putting $x$ and $y$ , replace them with parenthesis. HINT: 2. Put -6 for $x$ -parenthesis and 1 for $y$ -parenthesis in the parenthesis and click equals.
3. To convert decimal to fraction, click
3. Find the value of the expression if $\mathrm{x}=-1$ and $\mathrm{y}=6$ . $\frac{x y}{2}$ $\begin{array}{lll}\text { a. }-3 & \text { b. } 3 & \text { C. }-6 / 2\end{array}$ C. $-6 / 2$ D. $6 / 2$
1. Type the given expression in Desmos Scientific Calculator (not graphing) but instead of putting $x$ and $y$ , replace them with parenthesis. HINT:
2. Put -1 for $x$ -parenthesis and 6 for $y$ -parenthesis in the parenthesis and click equals.
3. To convert decimal to fraction, click
4. Are these expressions equivalent? $\frac{2 s}{3 t} \quad \frac{4 s}{6 t}$ a. Nonequivalent b. Equivalent c. both a and b d. None of the choices
HINT: Reduce the fractions to lowest terms if they are the same.
5. What sign? a. 6 b. 13 c. $t$ d. 7
HINT: Add the numerators 6 and 7 . $\frac{6}{t}+\frac{7}{t}=\frac{?}{t}$

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Problem 1184

\begin{align} &\text{7) Trouver le domaine de définition de } f(x) = 2x. \\ &\text{8) Trouver le domaine de définition de } f(x) = \frac{3x}{x^2 - 2x + 1}. \\ &\text{9) Trouver le domaine de définition de } f(x) = \frac{2}{x(x+1)}. \\ &\text{10) Trouver le domaine de définition de } f(x) = \frac{x+4}{x+1}. \end{align}

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Problem 1185

Solve the inequality. (Enter your answer using $\frac{x^{2}-16}{x^{4}-16}<0$

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Problem 1186

b) $\frac{1}{2 x}-\frac{2}{5}=\frac{1}{10 x}$

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Problem 1187

Divide. $\frac{3 b y}{2 y^{4}} \div \frac{15 b}{8 y}$

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Problem 1188

$\frac{20x^{2} + 7x - 3}{20x^{2} - 13x + 2}$

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Problem 1189

4. $133 \div y=19 \quad y=6,7,8,9$

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Problem 1190

6. $\frac{x^{2}+11 x+30}{x^{2}+2 x-24}$

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Problem 1191

Find all real solutions of the following rational equation and check any results. $\frac{1}{x-5}+\frac{1}{x+5}=\frac{-10}{x^{2}-25}$
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution(s) is/are $\square$ and the extraneous solution(s) is/are $\square$ . (Type exact answers, using radicals as needed. Use a comma to separate answers as needed.) B. The solution(s) is/are $\square$ and there are no extraneous solutions. (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) C. There are no real solutions, but an extraneous solution of $\square$ (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) D. There are no real solutions and no extraneous solutions.

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Problem 1192

Solve the rational equation: $\frac{5}{x^{2}-49}=\frac{6}{x-7}-\frac{4}{x+7}$

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Problem 1193

4) $\frac{5}{m-7}=\frac{4}{m-9}$

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Problem 1194

5. $\frac{13 x+120}{7 x-3}=\frac{2}{3}$

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Problem 1195

Exit Ticket: solve the equation for $x$ : $\left(\frac{12}{7 x}\right)+\left(\frac{3}{2 x}\right)=\left(\frac{15}{14}\right)$

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Problem 1196

olve each of the followi $\left(\frac{1}{6 b^{2}}\right)+\left(\frac{1}{6 b}\right)=\left(\frac{1}{b^{2}}\right)$

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Problem 1197

f. $\frac{12 x^{2} y^{3} z}{6 x^{3} y^{2} z^{2}}$

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Problem 1198

Question Solve: $-\left(\frac{2}{3} a-\frac{1}{3}\right)+\frac{5}{3} a=-\frac{1}{3}$ .

See Solution

Problem 1199

Identify the restrictions on the domain of $f(x)=\frac{x-3}{x+5}$ $x \neq 5$ $x \neq-5$ $x=3$ $x \neq-3$

See Solution

Problem 1200

Use the following information to answer the next question. Consider the following rational equation. $\frac{x-3}{10}=4 x$
How many non-permissible values does this rational equation have? Select one: a. 0 b. 1 c. 3 d. 2
Use the following information to answer the next question.

See Solution

Rational

Problem 1101

Problem 1102

x+5x+7x(x+8)=\frac{x+5}{x} + \frac{7}{x(x+8)} =xx+5​+x(x+8)7​=

Problem 1103

Analyzing and graphing rational functions.pdf Download Analyzing and graphing rational functions.pdf (414 KB) Page 84. f(x)=2x2x2−1f(x)=\frac{2 x^{2}}{x^{2}-1}f(x)=x2−12x2​

Problem 1104

所 36=89\frac{\text { 所 }}{36}=\frac{8}{9}36 所 ​=98​

Problem 1105

Evaluate the expression for the given variable value. 2r=342r = \frac{3}{4}2r=43​; r=32r = \frac{3}{2}r=23​ (Type a whole number, fraction, or mixed number.)

Problem 1106

−59(k+2)=−2-\frac{5}{9}(k+2)=-2−95​(k+2)=−2Write your answer as a fraction k=k=k=

Problem 1107

Problem 1108

20. A student walks 3 km to school in 40 minutes and then runs 3 km back in 20 minutes. What is their average velocity for the round trip?

Problem 1109

Find the holes of the function f(x)=(x+4)(x−2)(x−5)(x−2) f(x) = \frac{(x+4)(x-2)}{(x-5)(x-2)} f(x)=(x−5)(x−2)(x+4)(x−2)​.

Problem 1110

Problem 1111

f(x)=7xx−4f(x) = \frac{7x}{x-4}f(x)=x−47x​The equation(s) of the vertical asymptote(s) is/are x=4x = 4x=4.The equation(s) of the horizontal asymptote(s) is/are y=7y = 7y=7.f(x)=7xx−4f(x) = \frac{7x}{x-4}f(x)=x−47x​

Problem 1112

Solve for x using cross multiplication. x−32=x−43x=[?]\begin{array}{c} \frac{x-3}{2}=\frac{x-4}{3} \\ x=[?] \end{array}2x−3​=3x−4​x=[?]​ Enter

Problem 1113

Problem 1114

MATH-1314-61408-College Algebra nework: Practice Final Exam - Homework Question 2,Find the domain of the function. f(x)=x+76−xf(x)=\frac{x+7}{6-x}f(x)=6−xx+7​

Problem 1115

Solve the following equation for qqq:10q−7=6q\frac{10}{q-7} = \frac{6}{q}q−710​=q6​q=q = q=Help: If there is more than one correct answer, enter your answers as a comma separated list. If the equation has no real solution, write "No Solution."

Problem 1116

Perform the operation and simplify the result when possible. xx2+5x+6+xx2−4\frac{x}{x^2 + 5x + 6} + \frac{x}{x^2 - 4}x2+5x+6x​+x2−4x​ Submit Answer

Problem 1117

Problem 1118

4. Mary and Joe can complete a job together in 6 hours. Mary can do the job in 14 hours working alone. How long would it take Joe to complete the job if he is working alone?

Problem 1119

Simplify. 6u3w42u3v2+10u\frac{6u^3 w^4}{2u^3 v^2 + 10u}2u3v2+10u6u3w4​

Problem 1120

f(x)=3x+3x+2f(x) = \frac{3x+3}{x+2}f(x)=x+23x+3​Graph the rational function.Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.

Problem 1121

Problem 1122

a) 7q−2⋅2q−4q+4\frac{7}{q-2} \cdot \frac{2 q-4}{q+4}q−27​⋅q+42q−4​

Problem 1123

Problem 1124

Problem 1125

(c) 14m÷(−2m)=14m \div (-2m)=14m÷(−2m)=

Problem 1126

Problem 1127

Solve the formula N=UPU+9N=\frac{U P}{U+9}N=U+9UP​ for the variable PPP. P=P=P=

Problem 1128

Find the partial fraction decomposition for the rational expression. −31x−852x2+13x+20\frac{-31x - 85}{2x^2 + 13x + 20}2x2+13x+20−31x−85​

Problem 1129

(b) 3b+27b−2−3b+22−7b\frac{3b+2}{7b-2} - \frac{3b+2}{2-7b}7b−23b+2​−2−7b3b+2​14. Simplify.(a) 4x2−3x+xx2+2x−15\frac{4}{x^2 - 3x} + \frac{x}{x^2 + 2x - 15}x2−3x4​+x2+2x−15x​(b) xx2−4−3x2−2x\frac{x}{x^2 - 4} - \frac{3}{x^2 - 2x}x2−4x​−x2−2x3​15. Simplify

Problem 1130

Problem 1131

f(x)=∣x−5∣⋅xx(x2+14x−95)f(x) = \frac{|x - 5| \cdot x}{x(x^2 + 14x - 95)}f(x)=x(x2+14x−95)∣x−5∣⋅x​

Problem 1132

Problem 1133

Find "a" and "b" so that the equation produces the graph below. y=axx+ba=□b=□\begin{array}{l} y=\frac{a x}{x+b} \\ a=\square \\ b=\square \end{array}y=x+bax​a=□b=□​

Problem 1134

Problem 1135

−13(x+y)+23(x+y) -\frac{1}{3}(x+y) + \frac{2}{3}(x+y) −31​(x+y)+32​(x+y)

Problem 1136

−13(x+y)+23(x+y) -\frac{1}{3}(x+y) + \frac{2}{3}(x+y) −31​(x+y)+32​(x+y)

Problem 1137

Divide. 37x2−q÷2121x2−3q\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}7x2−q3​÷21x2−3q21​ 37x2−q÷2121x2−3q=\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}=7x2−q3​÷21x2−3q21​= □\square□ (Simplify your answer.)

Problem 1138

Simplify:? (2x2+5x+2x+1)(x2−1x+2)\left(\frac{2x^2 + 5x + 2}{x + 1}\right)\left(\frac{x^2 - 1}{x + 2}\right)(x+12x2+5x+2​)(x+2x2−1​)

Problem 1139

Add. The numerator should be expanded and simplified. The denominator should be either expanded or factored. 2x−4+9x+3=\frac{2}{x-4} + \frac{9}{x+3} = x−42​+x+39​=

Problem 1140

Simplify the expression. 4x−43x−15\frac{4 x-4}{3 x-15}3x−154x−4​Select the correct choice below and fill in any A. 4x−43x−15=\frac{4 x-4}{3 x-15}=3x−154x−4​= □\square□ B. The expression cannot be simplified.

Problem 1141

Problem 1142

H3/(G3∗G4∗(1+G3∗G4∗H2))H_3 / (G_3 * G_4 * (1 + G_3 * G_4 * H_2))H3​/(G3​∗G4​∗(1+G3​∗G4​∗H2​))

Problem 1143

y=6−x−x3−9y=\frac{6-x}{-x^{3}-9}y=−x3−96−x​

Problem 1144

f(x)=2x2+2xx2−2x−3f(x) = \frac{2x^2 + 2x}{x^2 - 2x - 3}f(x)=x2−2x−32x2+2x​ What are the coordinates of the hole, if one exists. (-1, -2) (-1, 12\frac{1}{2}21​) there isn't one (-1, −12-\frac{1}{2}−21​)

Problem 1145

Problem 1146

Solve each equation. Remember to check for extraneous solutions.11) a−66a2=16a2+a+53a2\frac{a-6}{6a^2} = \frac{1}{6a^2} + \frac{a+5}{3a^2}6a2a−6​=6a21​+3a2a+5​

Problem 1147

$\frac{x+5}{x} + \frac{7}{x(x+8)} =$

Analyzing and graphing rational functions.pdf Download Analyzing and graphing rational functions.pdf (414 KB) Page 8
4. $f(x)=\frac{2 x^{2}}{x^{2}-1}$

$\frac{\text { 所 }}{36}=\frac{8}{9}$

Evaluate the expression for the given variable value. $2r = \frac{3}{4}$ ; $r = \frac{3}{2}$ (Type a whole number, fraction, or mixed number.)

$-\frac{5}{9}(k+2)=-2$
Write your answer as a fraction $k=$

Find the holes of the function $f(x) = \frac{(x+4)(x-2)}{(x-5)(x-2)}$ .

$f(x) = \frac{7x}{x-4}$
The equation(s) of the vertical asymptote(s) is/are $x = 4$ .
The equation(s) of the horizontal asymptote(s) is/are $y = 7$ .
$f(x) = \frac{7x}{x-4}$

Solve for x using cross multiplication. $\begin{array}{c} \frac{x-3}{2}=\frac{x-4}{3} \\ x=[?] \end{array}$ Enter

MATH-1314-61408-College Algebra nework: Practice Final Exam - Homework Question 2,
Find the domain of the function. $f(x)=\frac{x+7}{6-x}$

Solve the following equation for $q$ :
$\frac{10}{q-7} = \frac{6}{q}$
$q =$
Help: If there is more than one correct answer, enter your answers as a comma separated list. If the equation has no real solution, write "No Solution."

Perform the operation and simplify the result when possible. $\frac{x}{x^2 + 5x + 6} + \frac{x}{x^2 - 4}$ Submit Answer

Simplify. $\frac{6u^3 w^4}{2u^3 v^2 + 10u}$

$f(x) = \frac{3x+3}{x+2}$
Graph the rational function.
Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.

a) $\frac{7}{q-2} \cdot \frac{2 q-4}{q+4}$

(c) $14m \div (-2m)=$

Solve the formula $N=\frac{U P}{U+9}$ for the variable $P$ . $P=$

Find the partial fraction decomposition for the rational expression. $\frac{-31x - 85}{2x^2 + 13x + 20}$

(b) $\frac{3b+2}{7b-2} - \frac{3b+2}{2-7b}$
14. Simplify.
(a) $\frac{4}{x^2 - 3x} + \frac{x}{x^2 + 2x - 15}$
(b) $\frac{x}{x^2 - 4} - \frac{3}{x^2 - 2x}$
15. Simplify

$f(x) = \frac{|x - 5| \cdot x}{x(x^2 + 14x - 95)}$

Find "a" and "b" so that the equation produces the graph below. $\begin{array}{l} y=\frac{a x}{x+b} \\ a=\square \\ b=\square \end{array}$

$-\frac{1}{3}(x+y) + \frac{2}{3}(x+y)$

$-\frac{1}{3}(x+y) + \frac{2}{3}(x+y)$

Divide. $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}$ $\frac{3}{7 x^{2}-q} \div \frac{21}{21 x^{2}-3 q}=$ $\square$ (Simplify your answer.)

Simplify:? $\left(\frac{2x^2 + 5x + 2}{x + 1}\right)\left(\frac{x^2 - 1}{x + 2}\right)$

Add. The numerator should be expanded and simplified. The denominator should be either expanded or factored. $\frac{2}{x-4} + \frac{9}{x+3} =$

Simplify the expression. $\frac{4 x-4}{3 x-15}$
Select the correct choice below and fill in any A. $\frac{4 x-4}{3 x-15}=$ $\square$ B. The expression cannot be simplified.

$H_3 / (G_3 * G_4 * (1 + G_3 * G_4 * H_2))$

$y=\frac{6-x}{-x^{3}-9}$

$f(x) = \frac{2x^2 + 2x}{x^2 - 2x - 3}$ What are the coordinates of the hole, if one exists. (-1, -2) (-1, $\frac{1}{2}$ ) there isn't one (-1, $-\frac{1}{2}$ )

Solve each equation. Remember to check for extraneous solutions.
11) $\frac{a-6}{6a^2} = \frac{1}{6a^2} + \frac{a+5}{3a^2}$

4. What value of $r$ makes this equation true? $336 \div r=48$ a. 7 b. 6 c. 8 d. 9

2) $\frac{7x^2 + 35x}{x + 5}$

Solve for $v$ .
$\frac{4}{5v - 20} - 3 = -\frac{8}{v - 4}$
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

$S + \frac{17}{6} = \frac{57}{7}$

1) Evaluate $\frac{2}{5}k - 3.5$ for $k = 15$ .

1 Find the slant asymptote of the function $f(x)=\frac{x^{2}+4 x-8}{x+3}$ ?

Write the form of the partial fraction decomposition of the rational expression given below. Do not solve for the constants. $\frac{x-5}{x^2 + 9x + 18}$

Find the vertical asymptotes. $g(r)=\frac{r-7}{r^{2}-2 r-8}$
Enter your answers in increasing order. $\begin{array}{l} r= \\ r= \end{array}$

Which values are NOT in the domain of the rational function? $f(x) = \frac{(x - 1)(x + 2)}{x^2 - 9}$

Identify the vertical asymptote(s) of the rational function. $f(x) = \frac{x(x+6)(x-10)}{(x-5)(x+6)}$

(d) $\frac{x^2 - 3x + 2}{x^3 + 4x} \le 0$
When does the graph of $\frac{x^2 + 2x - 4}{x(x-2)^2}$ lie above the graph of $\frac{2}{x(x-2)}$ ?
3. Logarithmic Functions

30. Solve: $\frac{x+3}{x^{2}+5 x+6}=\frac{3}{2 x+4}-\frac{1}{x+3}$

What mass of NaCl are dissolved in 152 mL of a solution if the concentration of the solution is $0.364$ M? $3.24$ g of NaCl will be required

Add and simplify: $\frac{2}{x+9} + \frac{x+45}{x^2 - 81}$

$\mathrm{A} = \frac{\mathrm{r}}{2 \mathrm{~L}}$ Solve for $L$ .

Simplify the complex rational expression using either Method I or Method II. $\frac{\frac{y}{2} - \frac{2}{y}}{\frac{2}{y^2} - \frac{1}{2}} = \text{?}$

For the following expression, find the correct partial fraction decomposition for $\frac{3 x^{2}+22 x+1}{(5 x+3)\left(x^{2}-2 x+4\right)}$
Provide your answer below: $\square$ $+$ $\square$

Question For the following expression, find the correct partial fraction decomposition. $\frac{-z^{3}-z^{2}+z-5}{\left(z^{2}+2\right)\left(z^{2}+2\right)}$

For the following expression, find the correct partial fraction decomposition. $\frac{-3 y^{3}+10 y^{2}-20 y+3}{\left(y^{2}-3 y+5\right)\left(y^{2}-3 y+5\right)}$