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: 43

Answer

$\displaystyle \frac{(x-2)^{2}}{x}$

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}\div\frac{x+2}{x-2}=\frac{x^{2}-4}{x}\cdot\frac{x-2}{x+2}\qquad$... factor what you can $=\displaystyle \frac{(x-2)(x+2)}{x}\cdot\frac{x-2}{x+2}\qquad$... divide out the common factors $=\displaystyle \frac{(x-2)\cdot 1}{x}\cdot\frac{(x-2)}{1}\qquad$ = $\displaystyle \frac{(x-2)^{2}}{x}$
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