Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 7 - Rational Functions - 7.3 Multiplying and Dividing Rational Expressions - 7.3 Exercises - Page 581: 41



Work Step by Step

$\frac{x^{2}-25}{x^{2}+7x+10} \div \frac{x^{2}-4}{x^{2}+9x+8}$ $= \frac{x^{2}-25}{x^{2}+7x+10} \times \frac{x^{2}+9x+8}{x^{2}-4}$ $= \frac{(x-5)(x+5)}{(x+5)(x+2)} \times \frac{(x+8)(x+1)}{(x-2)(x+2)}$ $= \frac{(x-5)}{(x+2)} \times \frac{(x+8)(x+1)}{(x-2)(x+2)}$ $=\frac{(x-5)(x+8)(x+1)}{(x-2)(x+2)(x+2)}$ $=\frac{(x-5)(x+8)(x+1)}{(x-2)(x+2)^{2}}$
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