Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set - Page 499: 12

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

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 $m$: $\dfrac{(m-n)^{2}}{m+n}\cdot\dfrac{m}{m^{2}-mn}=\dfrac{(m-n)^{2}}{m+n}\cdot\dfrac{m}{m(m-n)}=...$ Multiply the two rational expressions and simplify by removing the 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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