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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. 44 (page 652)

In the following exercises, divide the rational expressions.
$\frac{10 + w}{w - 8} 梅 \frac{100 - w^{2}}{8 - w}$

Short Answer

Expert verified

The solution is $\frac{- 1}{10 - w} .$

Step by step solution

01

Step 1. Given InformationFlip the second rational expression

We have

\frac{10 + w}{w - 8} 梅 \frac{100 - w^{2}}{8 - w} = \frac{10 + w}{w - 8} 脳 \frac{8 - w}{100 - w^{2}}

02

Step 2. Factor the numerators and denominators

$\frac{10 + w}{w - 8} 脳 \frac{8 - w}{(10 - w) (10 + w)} = \frac{- (10 + w) (w - 8)}{(w - 8) (10 - w) (10 + w)}$

03

Step 3. Remove the common factor and simplify

$= \frac{- 1}{10 - w}$

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