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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.498. (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 $R (x) = f (x) - g (x)$ .

Short Answer

Expert verified

The solution is $\frac{2 x - 9}{(x - 2) (x - 4) (x - 5)}$ .

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.

$R (x) = f (x) - g (x) R (x) = \frac{x - 4}{x^{2} - 3 x - 10} - \frac{x - 5}{x^{2} - 2 x - 8} R (x) = \frac{x - 4}{(x + 2) (x - 5)} - \frac{x - 5}{(x + 2) (x - 4)} R (x) = \frac{(x - 4) (x - 4) - (x - 5) (x - 5)}{(x + 2) (x - 5) (x - 4)} R (x) = \frac{x^{2} - 8 x + 16 - x^{2} + 10 x - 25}{(x + 2) (x - 5) (x - 4)} R (x) = \frac{- 8 x + 10 x - 25 + 16}{(x + 2) (x - 5) (x - 4)} R (x) = \frac{2 x - 9}{(x + 2) (x - 5) (x - 4)}$

03

Step 3. Simplified answer.

Hence, the simplified expression is $R (x) = \frac{2 x - 9}{(x + 2) (x - 5) (x - 4)}$ .

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Most popular questions from this chapter

Simplify the complex rational expression by writing it as division:

$\frac{\frac{1}{x} + \frac{1}{y}}{\frac{1}{x} - \frac{1}{y}}$

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