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Math  /  Algebra

QuestionSimplify the expression 2x−3x−2+3−xx−2\frac{2 x-3}{x-2}+\frac{3-x}{x-2} and give your answer in the form of f(x)g(x)\frac{f(x)}{g(x)}.
Your answer for the function f(x)f(x) is : □\square Your answer for the function g(x)g(x) is : □\square Question Help: □\square Message instructor Submit Question
Question 9 0/20 / 2 pts 3 99 Details
Subtract and simplify: x2+21xx+6−21x+36x+6\frac{x^{2}+21 x}{x+6}-\frac{21 x+36}{x+6} □\square

Studdy Solution

STEP 1

1. The expression involves two rational expressions with the same denominator.
2. Simplification involves combining the numerators over the common denominator.
3. The result should be expressed in the form f(x)g(x)\frac{f(x)}{g(x)}.

STEP 2

1. Combine the numerators of the fractions.
2. Simplify the resulting expression.

STEP 3

Identify the common denominator in the expression:
Both fractions have the same denominator x−2x-2.
2x−3x−2+3−xx−2=(2x−3)+(3−x)x−2 \frac{2x-3}{x-2} + \frac{3-x}{x-2} = \frac{(2x-3) + (3-x)}{x-2}
Combine the numerators:
(2x−3)+(3−x)=2x−3+3−x (2x-3) + (3-x) = 2x - 3 + 3 - x

STEP 4

Simplify the combined numerator:
2x−3+3−x=2x−x=x 2x - 3 + 3 - x = 2x - x = x
Thus, the expression becomes:
xx−2 \frac{x}{x-2}
The simplified expression is:
Your answer for the function f(x)f(x) is: xx
Your answer for the function g(x)g(x) is: x−2x-2

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