Answer
$\displaystyle \frac{2(m-n)}{mn(m+n^{2})}$
Work Step by Step
$\displaystyle \frac{2n^{-1}-2m^{-1}}{m+n^{2}}$=.........$\displaystyle \frac{1}{a^{n}}=a^{-n}$ ........
$=\displaystyle \frac{\frac{2}{n}-\frac{2}{m}}{m+n^{2}}$=.........in ($\displaystyle \frac{2}{n}-\frac{2}{m}$): comm. denom. =nm
$=\displaystyle \frac{\frac{2m}{nm}-\frac{2n}{nm}}{m+n^{2}}$=.........factor out $\displaystyle \frac{2}{nm}$ from the numerator.......
=$\displaystyle \frac{2}{nm}\cdot\frac{m-n}{m+n^{2}}$
$=\displaystyle \frac{2(m-n)}{mn(m+n^{2})}$
