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:
$...=\dfrac{m(m-n)(m+n)^{2}}{m(m+n)}=(m-n)(m+n)$
