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: 14

Answer

$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}=\dfrac{a+3}{a+2}$

Work Step by Step

$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}$ Factor the numerator and the denominator of the first fraction: $\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}=\dfrac{(a-2)^{2}}{(a-2)(a+2)}\cdot\dfrac{a+3}{a-2}=...$ Multiply the two rational expressions and simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{(a-2)^{2}(a+3)}{(a-2)^{2}(a+2)}=\dfrac{a+3}{a+2}$
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