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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q.499. (page 742)

Given $f (x) = \frac{x - 4}{x^{2} - 3 x - 10}$ and $g (x) = \frac{x - 5}{x^{2} - 2 x - 8}$ .
Find $R (x) = f (x) 路 g (x)$ .

Short Answer

Expert verified

The solution is $\frac{1}{(x + 2) (x + 2)}$ .

Step by step solution

01

Step 1. Given information.

The given functions are $f (x) = \frac{x - 4}{x^{2} - 3 x - 10}$ and $g (x) = \frac{x - 5}{x^{2} - 2 x - 8}$ .

02

Step 2. Simplify the rational expression.

$R (x) = f (x) 路 g (x) R (x) = \frac{x - 4}{x^{2} - 3 x - 10} 路 \frac{x - 5}{x^{2} - 2 x - 8} R (x) = \frac{(x - 4)}{(x + 2) (x - 5)} 路 \frac{(x - 5)}{(x + 2) (x - 4)} (R e m o v e t h e c o m m o n f a c t o r) R (x) = \frac{1}{(x + 2) (x + 2)}$

03

Step 3. Simplified answer.

Hence, the simplified expression is $\frac{1}{(x + 2) (x + 2)}$ .

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Most popular questions from this chapter

Divide the rational expression $\frac{3 y^{2} - 12 y - 63}{4 y + 3} 梅 (6 y^{2} - 42 y)$

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In the following exercises, multiply the rational expressions.

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