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: 52



Work Step by Step

Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$ $\displaystyle \frac{x^{2}-4}{x^{2}+3x-10}\div\frac{x^{2}+5x+6}{x^{2}+8x+15}=\frac{x^{2}-4}{x^{2}+3x-10}\cdot\frac{x^{2}+8x+15}{x^{2}+5x+6}\qquad$... factor what you can $x^{2}-4=(x+2)(x-2)$ $x^{2}+3x-10=(x+5)(x-2)$ $x^{2}+8x+15=(x+5)(x+3)$ $x^{2}+5x+6=(x+2)(x+3)$ $=\displaystyle \frac{(x+2)(x-2)}{(x+5)(x-2)}\cdot\frac{(x+5)(x+3)}{(x+2)(x+3)} \qquad$... divide out the common factors $=\displaystyle \frac{(1)(1)}{(1)(1)}\cdot\frac{(1)(1)}{(1)(1)} $ = $1$
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