Rational

Problem 701

5. $\frac{1}{6}+\frac{1}{6 a}=\frac{2}{a}$

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Problem 702

Simplify to the lowest terms and leave your answers as proper or improper fractions when necessary (ie $-\frac{2}{5} \longrightarrow-2 / 5$ ). $3(12-7)^{2}=$ type your answer...

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Problem 703

(b) Find the solution set for the inequality $\frac{-4-x}{x-3} \geq x+4$ . [6 marks]

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Problem 704

A small bottle weighs 20 gm when empty and 22 gm when filled with water. When it is filled with oil it weighs 21.76 gm . Then the density of the oil is (A) $0.88 \mathrm{~g} / \mathrm{cm}^{3}$ (B) $8.8 \mathrm{~g} / \mathrm{cm}^{3}$ (C) $6.8 \mathrm{~g} / \mathrm{cm}^{3}$ (D) $88.8 \mathrm{~g} / \mathrm{cm}^{3}$

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Problem 705

авсан бэ? 21 Компани 80 сая төгрөгийн ашиттай ажиллажээ. Ашгаа гурван хөрөнге оруулагч нь анх оруулсан торөнгөт эйтоо пропорциопалаар хувааж авав. Арвин 20 сая. Баян 35 сая, Ашид 25 сая төгрөг хөрөнгө оруулсан бол тэд ашгаа хэрхэн хуваасан бэ?

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Problem 706

Q18) Find the values of $(x)$ which $f(x)=\frac{x-3}{|x|-3}$ that not continuous and determine whether discontinuity is removable? a)3 b) -3 c) 0 d) $\{3,-3\}$

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Problem 707

$\frac{-4 x+1}{5 x+4}>-\frac{3}{2}$

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Problem 708

13. Given that the function $g(t)=\frac{u^{4}+4}{22^{2}+4 t a}$ has two different vertical asymptote, the value of a should satisfies A. $a \geq 2$ B. $a \leq 2$ C. $a<2$ D. $a>2$

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Problem 709

$\frac{x+4}{2 x-2} \div \frac{2 x^{2}+13 x+20}{4 x^{2}-4 x}$ answer as a single fraction in its simplest form

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Problem 710

$\frac{1}{4}=\frac{\square}{16}$

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Problem 711

$2 / 3(9 a+6 b)+1 / 4(4 a+8 b)$

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Problem 712

$216^{\frac{1}{3}}=$

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Problem 713

1. Jate asymptotes of the function $f(x)=\frac{3 x^{2}-5}{4 x^{2}-1}$

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Problem 714

Use the graph shown to find the following. (a) The domain and range of the function (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any

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Problem 715

Simplify by rationalizing the denominator. $\frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}$ $\square$

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Problem 716

Which of the following rational inequalities requires the use of technology to solve? a) $\frac{1}{x+5}>7$ b) $\frac{1}{x+5}>\frac{7}{x+1}$ C) $\frac{1}{x+5}>\frac{7 x^{2}}{x+1}$ d) B and C

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Problem 717

(2) $\frac{3 x-2}{3}-\frac{2 x+1}{4}=$

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Problem 718

Use the graph of $f(x)=\frac{5}{x^{2}+1}$ to solve the inequality $\frac{5}{x^{2}+1} \leq 1$ . a) $x= \pm 2$ b) no solution C) $-2 \leq x \leq 2$ d) $x \leq-2, x \geq 2$

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Problem 719

Adobe Acrobat Counting and Probability Factorial expressions
Evaluate. $\frac{5!7!}{3!6!}$
Simplify your answer as much as possible. $\square$ Explanation Check

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Problem 720

40. $\frac{a}{b}=\frac{2}{5}$ бол $\frac{5 a+b}{b}=$ ?
лахин бага вэ?

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Problem 721

Solve the proportion. (Simplify your answer completely.) $x=\frac{3}{x}=\frac{1}{32}$ Need Help? Read It Submit Answer

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Problem 722

Solve the proportion. (Simplify your answer completely.) $y=\quad \frac{10}{17}=\frac{y}{85}$ Need Help? Read It

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Problem 723

XII. Харьцаа, пропгорц
46. $\frac{a-2 b+c}{3 c-5 b}=\frac{1}{3}$ бол $\frac{b}{a}=$ ?

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Problem 724

4 $\qquad$ olifie les expressions suivantes.

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Problem 725

$\text{At } 21^{\circ} \mathrm{C}, \text{ a gas cylinder containing carbon monoxide has an internal volume and pressure of } 46.6 \, \text{L and } 1.50 \times 10^2 \, \text{atm}. \text{ What mass of nitrogen gas is contained in the cylinder?}$

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Problem 726

40. $\frac{a}{b}=\frac{2}{5}$ бол $\frac{5 a+b}{b}=$ ?

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Problem 727

$75-\frac{125}{3}-25-3=\frac{1}{3}-5$

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Problem 728

$\frac{1}{4}=\frac{3}{\square}$

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Problem 729

$\frac{1}{2}=\frac{8}{\square}$

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Problem 730

Find the partial fraction decomposition of the given rational expression. $\frac{6}{x(x-3)}$

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Problem 731

При каком значении переменной выражение НЕ имеет смысла?
Запиши в каждое поле для ответа верное число. $\frac{5-\mathrm{a}}{\mathrm{a}} \text { при } \mathrm{a}=0$ $\frac{3 \mathrm{~m}+1}{-2+\mathrm{m}} \text { при } \mathrm{m}=$ $-2$ $\frac{2 \mathrm{x}}{4+\mathrm{x}} \text { при } \mathrm{x}=$ $-4$

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Problem 732

Find the value of $a$ in this pair of equivalent fractions: $\frac{3}{4}=\frac{12}{a}$

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Problem 733

Solve $\frac{x-1}{x+1}-\frac{6}{x-1}=1$

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Problem 734

$\frac{3 x}{2 x+10}=1+\frac{1}{x+5}$

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Problem 735

(5) $\frac{x-1}{3}+\frac{x-4}{6}=$

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Problem 736

Add and/or subtract and then simplify completely: $\frac{5 r}{r^{2}-9}+\frac{8}{r-3}$
Enter the numerator and denominator separately in the boxes below. If the denominator is 1 , enter the number 1. Do not leave either box blank. Answer: $\square$ $\square$ Numerator preview: Denominator preview:

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Problem 737

(9) $\frac{-x+3}{6}+\frac{5 x-6}{12}=$

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Problem 738

Simplify $\frac{x-3}{x-4}-\frac{6 x-16}{x^{2}-16}$

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Problem 739

$\begin{array}{l}\frac{-1}{x+1}=\frac{4}{x+4} \\ x=\end{array}$

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Problem 740

(6) $\frac{2 x-3}{18}-\frac{2 x+1}{6}=$

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Problem 741

Solve the rational equation. Enter any solution that checks as an integer or reduced fraction. Separate with commas if there is more than one solution. If there are no solutions, click the No Solution button. $\frac{-3 a}{a^{2}-81}-\frac{5}{a-9}=\frac{1}{a+9}$ One or more solutions: $\square$ No solution

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Problem 742

(1) $\frac{4 x-1}{6}+\frac{4 x-5}{3}$

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Problem 743

$f(x) = \frac{-3x + 9}{x^2 - 8x + 15}$
Find the asymptotes, intercepts, and holes of the function $f(x)$ .

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Problem 744

Find the asymptotes, intercepts, and holes of the function $f(x) = \frac{5x^2 + 25x + 30}{3x + 6}$ .

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Problem 745

Given the function $f(x) = \frac{-2x-4}{x^2+5x+6}$ , find all the features needed to graph it.

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Problem 746

$\frac{x+3}{x+4}=\frac{24}{27}$

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Problem 747

$\text{Given the function } f(x) = \frac{4x^2 - 47x + 138}{x^2 - 11x + 30}, \text{ find the following:}$ \begin{itemize} \item Vertical asymptotes \item Horizontal asymptotes \item Slant asymptotes \item Intercepts \item Holes \end{itemize}

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Problem 748

The rational function $r$ is given by $r(x)=\frac{(x+1)^{2}(x-2)(x-1)}{x(x+1)(x-2)^{3}}$ . For which of the following values of $x$ does the graph of $r$ have vertical asymptotes?

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Problem 749

Simplify. $\frac{y^{2}-4 y-32}{2 y^{2}-4 y-48}$

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Problem 750

Exercice 6 Écris la règle sous sa forme canonique à trois paramètres ( $a, h$ et $k$ ). $f(x)=\frac{3 x+4}{4 x+5}$

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Problem 751

.4-4.6)
Graph the function $y=\frac{x^{2}-63}{x-8}$ by identifying the domain and any where the curve is increasing and where it is decreasing, finding as intercepts, critical points, and inflection points. Then find coord

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Problem 752

HA is a weak acid. A buffer containing 0.25 M HA and 0.50 MA - has a pH of 6.12. What is the Ka of the acid? $1.52 \times 10^{-6}$ 5.82 $7.59 \times 10^{-7}$ 6.12 $3.79 \times 10^{-7}$ $7.59 \times 10^{-5}$ none of the above

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Problem 753

8. $\frac{\frac{x^{2}}{\sqrt{x^{2}+2}}-\sqrt{x^{2}+2}}{x^{2}}$

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Problem 754

8. $\frac{\frac{x^{2}}{\sqrt{x^{2}+2}}-\sqrt{x^{2}+2}}{x^{2}}$

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Problem 755

Use the graph shown to find the following. (a) The domain and range of the function (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any (a) What is the domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of the function is $\{x \mid$ $\square$ \}. (Type an inequality in the form $x \neq$ . Use integers or fractions for any numbers in the expression. Use a comma to separate answers as neede B. The domain of the function is the set of all real numbers.
What is the range? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The range of the function is $\{y \mid$ $\square$ \}. (Type an inequality in the form $y \neq$ . Use integers or fractions for any numbers in the expression. Use a comma to separate answers as neede B. The range of the function is the set of all real numbers. b) Find the intercepts, if there are any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercent(s) is/are $\square$

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Problem 756

2. For each quotient, fill in the boxes to write three division statements that are true. (Knowledge and Understanding) a) $\square$ $\square$ $=+5$ $\square$ $\square$ $=+5$ $\square$ $\square$ $=+5$ b) $\begin{array}{l} \square \div \square=-3 \\ \square \div \square=-3 \\ \square \div \square=-3 \end{array}$ Matholonu 8 Onerations The rinht to renradure or madifu thic nane is rectricted to nurel

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Problem 757

Solve for $x$ . $2=-\frac{7}{x-4}$
Simplify your answer as much as possible. $x=$ No solution

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Problem 758

$f(x)=\frac{6 x^{2} \cdot \sqrt[3]{x^{5}}+4 x \cdot \sqrt[3]{x^{5}}-7 \cdot \sqrt[3]{x^{5}}}{5 \cdot \sqrt[3]{x^{5}}}$

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Problem 759

$=-\frac{1}{5}-\frac{\frac{1}{25}+\frac{1}{125}+2}{-\frac{3}{25}-\frac{2}{5}}$

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Problem 760

Solve $4 / x=20$ Write your answer as a decimal correct to 1 decimal place.

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Problem 761

$\frac{7}{10} b-\frac{3}{5} c+\frac{2}{5} b+\frac{1}{20} b-\frac{2}{10} c$

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Problem 762

$\frac{4 y-7}{25 x^{2}-30}=\frac{}{50 x^{2}-60}$ $\frac{4 y-7}{25 x^{2}-30}=\frac{\square}{50 x^{2}-60}$ (Simplify your answer. Do not factor.)

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Problem 763

Solve. Any solution is a real number. $\frac{x-6}{x-10}=\frac{4}{x-10}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\mathrm{x}=$ $\square$ (Simplify your answer. Use a comma to separate answers as needed.) B. The solution set is the empty set.

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Problem 764

Solve. All solutions is a real number. $\frac{x^{2}-37}{2 x^{2}-5 x-3}+\frac{4}{x-3}=\frac{-1}{2 x+1}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\mathrm{x}=$ $\square$ (Use a comma to separate answers as needed. Type exact answers, using radicals as needed.) B. The solution set is the empty set.

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Problem 765

Solve. Any solution is a real number. $3+\frac{2}{x}=\frac{6}{x^{2}}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\mathrm{x}=$ $\square$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The solution set is the empty set.

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Problem 766

1. $3 \frac{5}{7}+4 \frac{1}{4}=3+\frac{5 x}{7 x}+4+\frac{1 x}{4 x}$

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Problem 767

Petty Cash Fund
Journalize the necessary entries for each of the following: a. Issued a check to establish a petty cash fund of $\$ 1,270$ . If an amount box does not require an entry, leave it blank. Feedback
Check My Work a. Recall that the only time Petty Cash is used is when the fund is initially established or increased. b. The amount of cash in the petty cash fund is $\$ 160$ . Issued a check to replenish the fund, based on the following summary of petty cash receipts: store supplies, $\$ 780$ and miscellaneous selling expense, $\$ 280$ . Record any missing funds in the cash short and over account. If an amount box does not require an entry, leave it blank. Store Supplles Miscellaneous Selling Expense Cash Short and Over Cash $\square$ $\square$ $\checkmark$ $\square$ $\square$ $\checkmark$ $\square$ $\square$ $\checkmark$ $\square$ 1,110

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Problem 768

5. If $f(x)=\frac{5}{x+13}$ and $g(x)=\frac{8}{x+15}$ find $(f+g)(x)$ and state its domain.

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Problem 769

$\frac{2 x^{4}-3 x^{2}+4 x}{x-2}=\square+\frac{\square}{x-2}$

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Problem 770

Solve $\frac{3}{x-2}+\frac{21}{x^{2}-4}=\frac{14}{x+2}$ $x=1$ $x=2$
$\begin{array}{l} x=11 \\ x=5 \end{array}$

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Problem 771

The function $f$ is given by $f(x)=\frac{2^{2}-5 x+3}{x+2}$ . In the $x y$ plane, the graph of $f$ has a slant asymptote which of the following is an equation for the slant asymptote?

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Problem 772

NAME $\qquad$ Unit 5 Rational Test 1) Divide $\frac{a-6}{a-3} \div \frac{a+2}{a^{2}-8 a+15}$

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Problem 773

Exercise: Identifying Horizontal Asymptotes Algebraically
Answer
36. $s(x)=\frac{x+3}{2 x^{2}-3 x-5}$

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Problem 774

Solve the equation for the indicated variable. (Leave $\pm$ in the answer as needed.) $w=k s^{2} \text { for } s$

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Problem 775

3) For the function $Y(s)=\frac{s+4}{s^{2}(s+3)}=\frac{a}{s^{2}}+\frac{b}{s}+\frac{c}{s+3}$ determine the residues $\mathrm{a}, \mathrm{b}$ , and c. [2 Marks]

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Problem 776

Which is the rationalized form of the expression $\frac{\sqrt{\pi}}{\sqrt{x}+\sqrt{5}}$ ? a. $\frac{x}{x+5}$ c. $\frac{x-\sqrt{5 \pi}}{x-5}$ b. $\frac{x+\sqrt{5 \pi}}{x-5}$ d. $\frac{\sqrt{5 \pi}}{5}$
Please select the best answer from the choices provided A B C Mark this and return Save and Exit

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Problem 777

$\frac{5}{x+2}+\frac{3}{x-3}=2$

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Problem 778

$\frac{6}{9}=\frac{v}{6}$
Simplify your answer as much as possible. $v=$ $\square$

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Problem 779

$(n+n)(n-1)(n+1)$ Find the LCD of each group of fractions.
21. $\frac{1}{4}, \frac{5}{6}$
22. $\frac{1}{2}, \frac{3}{8}$
23. $\frac{3}{2}, \frac{2}{5}, \frac{1}{4}$
24. $\frac{2}{3}, \frac{5}{9}, \frac{1}{15}$
25. $\frac{5}{8}, \frac{2}{5}, \frac{4}{3}$
26. $\frac{2}{3}, \frac{3}{4}, \frac{5}{9}$ $\frac{6}{241}$
Find the LCD of each group of fractions.
27. $\frac{a+2 b}{4}, \frac{2 b-a}{6}$
28. $\frac{n-2}{12}, \frac{n+3}{15}$
29. $\frac{n-1}{15}, \frac{n+3}{20}$
36. $\frac{3}{2 x+10}, \frac{x}{5 x+25}$
37. $\frac{3 a}{a+1}, \frac{2}{a-1}$
38. $\frac{3}{a^{2}-4}, \frac{5}{a+2}$ implify.
7. $\frac{3}{n^{2}}+\frac{2}{n}$
18. $\frac{6}{x^{2} y}-\frac{4}{x y}$
19. $\frac{5}{2 x}-\frac{1}{4 x^{2}}$
20. $\frac{1}{3 x^{2}}+\frac{5}{6 x}$

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Problem 780

27. $\frac{3}{4(x+1)}+\frac{x}{x+1}$
High School of American Studies atgebraic Fractions Unit 4; Alge
28. $\frac{2 x}{x-1}+\frac{3}{2(x-1)}$
29. $\frac{4 n-3}{15}-\frac{3(n-2)}{10}$
Write each expression as a fraction in simplest form.
9. $6+\frac{1}{x}$
10. $2+\frac{5}{a}$
11. $3-\frac{2}{x}$
12. $5-\frac{3}{n}$
Write each expression as a fraction in simplest form.
17. $2+\frac{x}{y}$
18. $3-\frac{2}{x+1}$
19. $7+\frac{y}{y-2}$
Write each expression as a fraction in simplest form. $\begin{array}{ll}\text { 29. } \frac{x}{x-1}+\frac{x-1}{x}-2 & \text { 30. } x+\frac{2 x+1}{x-2}\end{array}$
31. $\frac{3}{x+1}+\frac{x}{x+1}-1$

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Problem 781

21 Multiple Choice 3 points Simplify, add, subtract, multiply or divide the rational expressions. Pay attention to signs so that you will know what operation should be performed. Don't forget to simplify at the end. $\frac{3 x^{2}-2 x-5}{x-2} \cdot \frac{x+10}{x+1} \cdot \frac{x-2}{x^{2}+x-90}$ $\frac{3 x-5}{x-9}$ $\frac{(3 x-5)(x+10)}{(x+9)(x-10)}$ $\frac{3 x+5}{x+9}$ $\frac{(3 x+5)(x-1)}{x+1}$

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Problem 782

```latex The graphic organizer is used to organize sets of real numbers. List the section that each number would belong in.
a) 0 $\qquad$ b) \sqrt{3} $\qquad$ c) \frac{8}{5} $\qquad$ d) \frac{14}{7} $\qquad$ e) \sqrt{25}
A is rational
B is integers
C is whole numbers
D is natural numbers
E is irrational

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Problem 783

The domain set of $f(x)=\frac{1}{3-\sqrt{x-2}}$ is

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Problem 784

Using the MACRS rates from the following table, what is the book value of a $\$ 4,000$ computer after 2 years? \begin{tabular}{|c|r|} \hline Year & MACRS Rate \\ \hline 1 & $20.0 \%$ \\ \hline 2 & $32.0 \%$ \\ \hline 3 & $19.2 \%$ \\ \hline 4 & $11.52 \%$ \\ \hline 5 & $11.52 \%$ \\ \hline 6 & $5.76 \%$ \\ \hline \end{tabular}
Book Value = \ $[?] Round to the nearest cent.$ \square$ Enter

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Problem 785

Test tremujori i parë Grupi A
1. Paraqite shprehjen si një thyesë të vetme në formë sa më të thjeshtë $\frac{x+1}{3}-\frac{x+2}{4}$ (2 pikë)

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Problem 786

Function f is defined by $f(x)=\frac{1}{b x+c}$ , where $b$ and $c$ are constants. The graph of $y=f(x)$ has a $y$ -intercept at $\left(0, \frac{5}{2}\right)$ . In the $x y$ -plane, the graph of $y=f(x-3)$ has a $y$ -intercept at $\left(0, \frac{1}{4}\right)$ . What is the value of $b$ ?

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Problem 787

The Nicols are buying a house selling for $\$ 355,000$ . They pay a down payment of $\$ 55,000$ from the sale of their current house. To obtain a 15 -year mortgage at a $6 \%$ interest rate, the Nicols must pay 2.5 points at the time of closing. a) What is the amount of the mortgage? b) What is the cost of the 2.5 points?

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Problem 788

15 Gegeben sind die Funktionen $f: x \mapsto \frac{6 x^{2}+5}{2 x}$ und $g: x \mapsto \frac{-2 x^{2}-2 x+5}{x}$ . Formen Sie die Funktionsterme $f(x)$ und $g(x)$ jeweils in eine Summe um und bestimmen Sie dann die Gleichungen der schrägen Asymptoten der Funktionsgraphen $\mathrm{G}_{\mathrm{f}}$ und $\mathrm{G}_{\mathrm{g}}$ .

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Problem 789

Suppose that the functions $g$ and $h$ are defined as follows. $\begin{array}{l} g(x)=x+4 \\ h(x)=(x+2)(x-4) \end{array}$ (a) Find $\left(\frac{g}{h}\right)(-3)$ . (b) Find all values that are NOT in the domain of $\frac{g}{h}$ .
If there is more than one value, separate them with commas. (a) $\left(\frac{g}{h}\right)(-3)=$ $\square$ (b) Value(s) that are NOT in the domain of $\frac{g}{h}$ : $\square$

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Problem 790

Suppose that the functions $g$ and $f$ are defined as follows. $\begin{array}{l} g(x)=(x-1)(x+2) \\ f(x)=7 x-4 \end{array}$ (a) Find $\left(\frac{g}{f}\right)$ (5). (b) Find all values that are NOT in the domain of $\frac{g}{f}$ .
If there is more than one value, separate them with commas.

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Problem 791

1. Find vertical \& Horizontal Asymp. of $f(x)=\frac{x}{3 x-2}$

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Problem 792

Ro. Ermitteln Sie jeweils eine gebrochen-rationale Funktion der Form $f: x \mapsto \frac{p(x)}{q(x)}$ , die bzw. deren Graph folgende Eigenschaften hat, und erläutern Sie sich gegenseitig Ihre Ergebnisse. a) Die Funktion $f$ divergiert für $x \rightarrow-\infty$ gegen $+\infty$ und der Funktionsgraph $G_{f}$ hat die Asymptote mit der Gleichung $x=-3$ . b) Der Funktionsgraph $\mathrm{G}_{\mathrm{f}}$ hat die Asymptote mit der Gleichung $\mathrm{x}=0,5$ und die Asymptote mit der Gleichung $y=4-3 x$ .

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Problem 793

3. Graph each of the following functions using: - The method of single roots, double roots, triple roots - The method of 'even' and 'odd' V. asymptotes - The direction towards the O.A. asymptote - You can cross the O.A. asymptote a) $y=\frac{x^{2}+1}{x}$ b) $y=\frac{(x-1)^{2}}{x}$ c) $y=\frac{(x+1)(x-1)^{2}}{x^{2}}$

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Problem 794

Evaluate. $64^{\frac{1}{3}}=$ $\square$ $16^{\frac{1}{4}}=$ $\square$

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Problem 795

Simplify completely $\frac{x^{2}-10 x-24}{x^{2}-3 x-108}$ and find the restrictions on the variable. $\frac{x+2}{x+9}, x \neq-2, x \neq-9$ $\frac{x+2}{x+9}, x \neq-9, x \neq 12$ $\frac{x-2}{x-9}, x \neq-2, x \neq-9$ $\frac{x-2}{x-9}, x \neq-9, x \neq 12$

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Problem 796

Multiply and simplify to lowest terms. $\frac{z^{2}-1}{z^{2}-36} \cdot \frac{z-6}{z+1}$

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Problem 797

Add and simplify to lowest terms. $\frac{y+2}{y-6}+\frac{8 y-56}{y-6}$

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Problem 798

$\frac{4x-1}{6} + \frac{4x-5}{3} = \frac{a-5b}{4} - \frac{3a-b}{6}$

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Problem 799

a $\frac{5}{2 x}+\frac{x+7}{x+4}=2$ b $\frac{2 x-3}{x+1}=\frac{x+6}{x-2}$ c $7-\frac{5}{x-2}=\frac{10}{x+2}$ d $\frac{x+5}{x+8}=1+\frac{6}{x+1}$

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Problem 800

Simplify. Rationalize the denominator. $\frac{9}{5-\sqrt{2}}$

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1 ...5 6 7 8 9 10 11 ...13

Rational

Problem 701

5. 16+16a=2a\frac{1}{6}+\frac{1}{6 a}=\frac{2}{a}61​+6a1​=a2​

Problem 702

Simplify to the lowest terms and leave your answers as proper or improper fractions when necessary (ie −25⟶−2/5-\frac{2}{5} \longrightarrow-2 / 5−52​⟶−2/5 ). 3(12−7)2=3(12-7)^{2}=3(12−7)2= type your answer...

Problem 703

(b) Find the solution set for the inequality −4−xx−3≥x+4\frac{-4-x}{x-3} \geq x+4x−3−4−x​≥x+4. [6 marks]

Problem 704

Problem 705

Problem 706

Q18) Find the values of (x)(x)(x) which f(x)=x−3∣x∣−3f(x)=\frac{x-3}{|x|-3}f(x)=∣x∣−3x−3​ that not continuous and determine whether discontinuity is removable? a)3 b) -3 c) 0 d) {3,−3}\{3,-3\}{3,−3}

Problem 707

−4x+15x+4>−32\frac{-4 x+1}{5 x+4}>-\frac{3}{2}5x+4−4x+1​>−23​

Problem 708

13. Given that the function g(t)=u4+4222+4tag(t)=\frac{u^{4}+4}{22^{2}+4 t a}g(t)=222+4tau4+4​ has two different vertical asymptote, the value of a should satisfies A. a≥2a \geq 2a≥2 B. a≤2a \leq 2a≤2 C. a<2a<2a<2 D. a>2a>2a>2

Problem 709

x+42x−2÷2x2+13x+204x2−4x\frac{x+4}{2 x-2} \div \frac{2 x^{2}+13 x+20}{4 x^{2}-4 x}2x−2x+4​÷4x2−4x2x2+13x+20​ answer as a single fraction in its simplest form

Problem 710

14=□16\frac{1}{4}=\frac{\square}{16}41​=16□​

Problem 711

2/3(9a+6b)+1/4(4a+8b)2 / 3(9 a+6 b)+1 / 4(4 a+8 b)2/3(9a+6b)+1/4(4a+8b)

Problem 712

21613=216^{\frac{1}{3}}=21631​=

Problem 713

1. Jate asymptotes of the function f(x)=3x2−54x2−1f(x)=\frac{3 x^{2}-5}{4 x^{2}-1}f(x)=4x2−13x2−5​

Problem 714

Use the graph shown to find the following. (a) The domain and range of the function (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any

Problem 715

Simplify by rationalizing the denominator. 3m−5\frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}m​−5​3​​ □\square□

Problem 716

Which of the following rational inequalities requires the use of technology to solve? a) 1x+5>7\frac{1}{x+5}>7x+51​>7 b) 1x+5>7x+1\frac{1}{x+5}>\frac{7}{x+1}x+51​>x+17​ C) 1x+5>7x2x+1\frac{1}{x+5}>\frac{7 x^{2}}{x+1}x+51​>x+17x2​ d) B and C

Problem 717

(2) 3x−23−2x+14=\frac{3 x-2}{3}-\frac{2 x+1}{4}=33x−2​−42x+1​=

Problem 718

Use the graph of f(x)=5x2+1f(x)=\frac{5}{x^{2}+1}f(x)=x2+15​ to solve the inequality 5x2+1≤1\frac{5}{x^{2}+1} \leq 1x2+15​≤1. a) x=±2x= \pm 2x=±2 b) no solution C) −2≤x≤2-2 \leq x \leq 2−2≤x≤2 d) x≤−2,x≥2x \leq-2, x \geq 2x≤−2,x≥2

Problem 719

Adobe Acrobat Counting and Probability Factorial expressionsEvaluate. 5!7!3!6!\frac{5!7!}{3!6!}3!6!5!7!​Simplify your answer as much as possible. □\square□ Explanation Check

Problem 720

40. ab=25\frac{a}{b}=\frac{2}{5}ba​=52​ бол 5a+bb=\frac{5 a+b}{b}=b5a+b​= ?лахин бага вэ?

Problem 721

Solve the proportion. (Simplify your answer completely.) x=3x=132x=\frac{3}{x}=\frac{1}{32}x=x3​=321​ Need Help? Read It Submit Answer

Problem 722

Solve the proportion. (Simplify your answer completely.) y=1017=y85y=\quad \frac{10}{17}=\frac{y}{85}y=1710​=85y​ Need Help? Read It

Problem 723

XII. Харьцаа, пропгорц46. a−2b+c3c−5b=13\frac{a-2 b+c}{3 c-5 b}=\frac{1}{3}3c−5ba−2b+c​=31​ бол ba=\frac{b}{a}=ab​= ?

Problem 724

4 \qquad olifie les expressions suivantes.

Problem 725

Problem 726

40. ab=25\frac{a}{b}=\frac{2}{5}ba​=52​ бол 5a+bb=\frac{5 a+b}{b}=b5a+b​= ?

Problem 727

75−1253−25−3=13−575-\frac{125}{3}-25-3=\frac{1}{3}-575−3125​−25−3=31​−5

Problem 728

14=3□\frac{1}{4}=\frac{3}{\square}41​=□3​

Problem 729

12=8□\frac{1}{2}=\frac{8}{\square}21​=□8​

Problem 730

Find the partial fraction decomposition of the given rational expression. 6x(x−3)\frac{6}{x(x-3)}x(x−3)6​

Problem 731

Problem 732

Find the value of aaa in this pair of equivalent fractions: 34=12a\frac{3}{4}=\frac{12}{a}43​=a12​

Problem 733

Solve x−1x+1−6x−1=1\frac{x-1}{x+1}-\frac{6}{x-1}=1x+1x−1​−x−16​=1

Problem 734

3x2x+10=1+1x+5\frac{3 x}{2 x+10}=1+\frac{1}{x+5}2x+103x​=1+x+51​

Problem 735

(5) x−13+x−46=\frac{x-1}{3}+\frac{x-4}{6}=3x−1​+6x−4​=

Problem 736

Problem 737

(9) −x+36+5x−612=\frac{-x+3}{6}+\frac{5 x-6}{12}=6−x+3​+125x−6​=

Problem 738

Simplify x−3x−4−6x−16x2−16\frac{x-3}{x-4}-\frac{6 x-16}{x^{2}-16}x−4x−3​−x2−166x−16​

Problem 739

−1x+1=4x+4x=\begin{array}{l}\frac{-1}{x+1}=\frac{4}{x+4} \\ x=\end{array}x+1−1​=x+44​x=​

Problem 740

(6) 2x−318−2x+16=\frac{2 x-3}{18}-\frac{2 x+1}{6}=182x−3​−62x+1​=

Problem 741

Problem 742

(1) 4x−16+4x−53\frac{4 x-1}{6}+\frac{4 x-5}{3}64x−1​+34x−5​

Problem 743

5. $\frac{1}{6}+\frac{1}{6 a}=\frac{2}{a}$

Simplify to the lowest terms and leave your answers as proper or improper fractions when necessary (ie $-\frac{2}{5} \longrightarrow-2 / 5$ ). $3(12-7)^{2}=$ type your answer...

(b) Find the solution set for the inequality $\frac{-4-x}{x-3} \geq x+4$ . [6 marks]

Q18) Find the values of $(x)$ which $f(x)=\frac{x-3}{|x|-3}$ that not continuous and determine whether discontinuity is removable? a)3 b) -3 c) 0 d) $\{3,-3\}$

$\frac{-4 x+1}{5 x+4}>-\frac{3}{2}$

13. Given that the function $g(t)=\frac{u^{4}+4}{22^{2}+4 t a}$ has two different vertical asymptote, the value of a should satisfies A. $a \geq 2$ B. $a \leq 2$ C. $a<2$ D. $a>2$

$\frac{x+4}{2 x-2} \div \frac{2 x^{2}+13 x+20}{4 x^{2}-4 x}$ answer as a single fraction in its simplest form

$\frac{1}{4}=\frac{\square}{16}$

$2 / 3(9 a+6 b)+1 / 4(4 a+8 b)$

$216^{\frac{1}{3}}=$

1. Jate asymptotes of the function $f(x)=\frac{3 x^{2}-5}{4 x^{2}-1}$

Simplify by rationalizing the denominator. $\frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}$ $\square$

Which of the following rational inequalities requires the use of technology to solve? a) $\frac{1}{x+5}>7$ b) $\frac{1}{x+5}>\frac{7}{x+1}$ C) $\frac{1}{x+5}>\frac{7 x^{2}}{x+1}$ d) B and C

(2) $\frac{3 x-2}{3}-\frac{2 x+1}{4}=$

Use the graph of $f(x)=\frac{5}{x^{2}+1}$ to solve the inequality $\frac{5}{x^{2}+1} \leq 1$ . a) $x= \pm 2$ b) no solution C) $-2 \leq x \leq 2$ d) $x \leq-2, x \geq 2$

Adobe Acrobat Counting and Probability Factorial expressions
Evaluate. $\frac{5!7!}{3!6!}$
Simplify your answer as much as possible. $\square$ Explanation Check

40. $\frac{a}{b}=\frac{2}{5}$ бол $\frac{5 a+b}{b}=$ ?
лахин бага вэ?

Solve the proportion. (Simplify your answer completely.) $x=\frac{3}{x}=\frac{1}{32}$ Need Help? Read It Submit Answer

Solve the proportion. (Simplify your answer completely.) $y=\quad \frac{10}{17}=\frac{y}{85}$ Need Help? Read It

XII. Харьцаа, пропгорц
46. $\frac{a-2 b+c}{3 c-5 b}=\frac{1}{3}$ бол $\frac{b}{a}=$ ?

4 $\qquad$ olifie les expressions suivantes.

40. $\frac{a}{b}=\frac{2}{5}$ бол $\frac{5 a+b}{b}=$ ?

$75-\frac{125}{3}-25-3=\frac{1}{3}-5$

$\frac{1}{4}=\frac{3}{\square}$

$\frac{1}{2}=\frac{8}{\square}$

Find the partial fraction decomposition of the given rational expression. $\frac{6}{x(x-3)}$

Find the value of $a$ in this pair of equivalent fractions: $\frac{3}{4}=\frac{12}{a}$

Solve $\frac{x-1}{x+1}-\frac{6}{x-1}=1$

$\frac{3 x}{2 x+10}=1+\frac{1}{x+5}$

(5) $\frac{x-1}{3}+\frac{x-4}{6}=$

(9) $\frac{-x+3}{6}+\frac{5 x-6}{12}=$

Simplify $\frac{x-3}{x-4}-\frac{6 x-16}{x^{2}-16}$

$\begin{array}{l}\frac{-1}{x+1}=\frac{4}{x+4} \\ x=\end{array}$

(6) $\frac{2 x-3}{18}-\frac{2 x+1}{6}=$

(1) $\frac{4 x-1}{6}+\frac{4 x-5}{3}$

$f(x) = \frac{-3x + 9}{x^2 - 8x + 15}$
Find the asymptotes, intercepts, and holes of the function $f(x)$ .

Find the asymptotes, intercepts, and holes of the function $f(x) = \frac{5x^2 + 25x + 30}{3x + 6}$ .

Given the function $f(x) = \frac{-2x-4}{x^2+5x+6}$ , find all the features needed to graph it.

$\frac{x+3}{x+4}=\frac{24}{27}$

The rational function $r$ is given by $r(x)=\frac{(x+1)^{2}(x-2)(x-1)}{x(x+1)(x-2)^{3}}$ . For which of the following values of $x$ does the graph of $r$ have vertical asymptotes?

Simplify. $\frac{y^{2}-4 y-32}{2 y^{2}-4 y-48}$

Exercice 6 Écris la règle sous sa forme canonique à trois paramètres ( $a, h$ et $k$ ). $f(x)=\frac{3 x+4}{4 x+5}$

.4-4.6)
Graph the function $y=\frac{x^{2}-63}{x-8}$ by identifying the domain and any where the curve is increasing and where it is decreasing, finding as intercepts, critical points, and inflection points. Then find coord

8. $\frac{\frac{x^{2}}{\sqrt{x^{2}+2}}-\sqrt{x^{2}+2}}{x^{2}}$

8. $\frac{\frac{x^{2}}{\sqrt{x^{2}+2}}-\sqrt{x^{2}+2}}{x^{2}}$

Solve for $x$ . $2=-\frac{7}{x-4}$
Simplify your answer as much as possible. $x=$ No solution

$f(x)=\frac{6 x^{2} \cdot \sqrt[3]{x^{5}}+4 x \cdot \sqrt[3]{x^{5}}-7 \cdot \sqrt[3]{x^{5}}}{5 \cdot \sqrt[3]{x^{5}}}$

$=-\frac{1}{5}-\frac{\frac{1}{25}+\frac{1}{125}+2}{-\frac{3}{25}-\frac{2}{5}}$

Solve $4 / x=20$ Write your answer as a decimal correct to 1 decimal place.

$\frac{7}{10} b-\frac{3}{5} c+\frac{2}{5} b+\frac{1}{20} b-\frac{2}{10} c$

$\frac{4 y-7}{25 x^{2}-30}=\frac{}{50 x^{2}-60}$ $\frac{4 y-7}{25 x^{2}-30}=\frac{\square}{50 x^{2}-60}$ (Simplify your answer. Do not factor.)

1. $3 \frac{5}{7}+4 \frac{1}{4}=3+\frac{5 x}{7 x}+4+\frac{1 x}{4 x}$

5. If $f(x)=\frac{5}{x+13}$ and $g(x)=\frac{8}{x+15}$ find $(f+g)(x)$ and state its domain.

$\frac{2 x^{4}-3 x^{2}+4 x}{x-2}=\square+\frac{\square}{x-2}$

Solve $\frac{3}{x-2}+\frac{21}{x^{2}-4}=\frac{14}{x+2}$ $x=1$ $x=2$
$\begin{array}{l} x=11 \\ x=5 \end{array}$

The function $f$ is given by $f(x)=\frac{2^{2}-5 x+3}{x+2}$ . In the $x y$ plane, the graph of $f$ has a slant asymptote which of the following is an equation for the slant asymptote?

NAME $\qquad$ Unit 5 Rational Test 1) Divide $\frac{a-6}{a-3} \div \frac{a+2}{a^{2}-8 a+15}$

Exercise: Identifying Horizontal Asymptotes Algebraically
Answer
36. $s(x)=\frac{x+3}{2 x^{2}-3 x-5}$

Solve the equation for the indicated variable. (Leave $\pm$ in the answer as needed.) $w=k s^{2} \text { for } s$