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Intermediate Algebra

OPENSTAX

$Math Studyset 魅影直播 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 65 (page 653)

For the following exercises, find $R (x) = f (x) . g (x)$ where $f (x) a n d g (x)$ are given.
$f (x) = \frac{4 x}{x^{2} - 3 x - 10} a n d g (x) = \frac{x^{2} - 25}{8 x^{2}}$

Short Answer

Expert verified

The value of $R (x) = \frac{(x + 5)}{2 x (x + 2)}$

Step by step solution

01

Step 1. Given Information

$f (x) = \frac{4 x}{x^{2} - 3 x - 10} a n d g (x) = \frac{x^{2} - 25}{8 x^{2}}$

02

Step 2. Factor each numerator and denominator

$R (x) = \frac{4 x}{x^{2} - 3 x - 10} . \frac{x^{2} - 25}{8 x^{2}} R (x) = \frac{4 x}{(x - 5) (x + 2)} . \frac{(x - 5) (x + 5)}{8 x 脳 x} R (x) = \frac{4 x (x - 5) (x + 5)}{8 x . x (x - 5) (x + 2)}$

03

Step 3. Remove common factors and simplify

$R (x) = \frac{(x + 5)}{2 x (x + 2)}$

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Most popular questions from this chapter

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