Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set - Page 499: 44



Work Step by Step

Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$ $ \displaystyle \frac{x^{2}-4}{x-2}\div\frac{x+2}{4x-8}=\frac{x^{2}-4}{x-2}\cdot\frac{4x-8}{x+2}\qquad$... factor what you can $=\displaystyle \frac{(x-2)(x+2)}{x-2}\cdot\frac{4(x-2)}{x+2}\qquad$... divide out the common factors $=\displaystyle \frac{(1)(1)}{1}\cdot\frac{4(x-2)}{1}\qquad$ $=4(x-2)$ = $4x-8$
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