Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 39

Answer

$\dfrac{(x+2)^{2}}{x-2}\div\dfrac{x^{2}-4}{2x-4}=\dfrac{2(x+2)}{x-2}$

Work Step by Step

$\dfrac{(x+2)^{2}}{x-2}\div\dfrac{x^{2}-4}{2x-4}$ Factor the second fraction completely: $\dfrac{(x+2)^{2}}{x-2}\div\dfrac{x^{2}-4}{2x-4}=\dfrac{(x+2)^{2}}{x-2}\div\dfrac{(x-2)(x+2)}{2(x-2)}=...$ Evaluate the division of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{2(x-2)(x+2)^{2}}{(x-2)^{2}(x+2)}=\dfrac{2(x+2)}{x-2}$
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