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: 11

Answer

$\dfrac{(m+n)^{2}}{m-n}\cdot\dfrac{m}{m^{2}+mn}=\dfrac{m+n}{m-n}$

Work Step by Step

$\dfrac{(m+n)^{2}}{m-n}\cdot\dfrac{m}{m^{2}+mn}$ Factor the denominator of the second fraction by taking out common factor $m$: $\dfrac{(m+n)^{2}}{m-n}\cdot\dfrac{m}{m^{2}+mn}=\dfrac{(m+n)^{2}}{m-n}\cdot\dfrac{m}{m(m+n)}=...$ Multipy both rational expressions and simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{m(m+n)^{2}}{m(m+n)(m-n)}=\dfrac{(m+n)^{2}}{(m+n)(m-n)}=\dfrac{m+n}{m-n}$
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