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: 25

Answer

$\dfrac{m^{2}-n^{2}}{m+n}\div\dfrac{m}{m^{2}+nm}=(m-n)(m+n)$

Work Step by Step

$\dfrac{m^{2}-n^{2}}{m+n}\div\dfrac{m}{m^{2}+nm}$ Factor the numerator of the first fraction and take out common factor $m$ from the denominator of the second fraction: $\dfrac{m^{2}-n^{2}}{m+n}\div\dfrac{m}{m^{2}+nm}=\dfrac{(m-n)(m+n)}{m+n}\div\dfrac{m}{m(m+n)}=...$ Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator of the resulting expression: $...=\dfrac{m(m-n)(m+n)^{2}}{m(m+n)}=(m-n)(m+n)$
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