Answer
$\frac{y-x}{xy}$
Work Step by Step
We form a common denominator for the fractions in the numerator and denominator. After combining them, we switch from division to multiplication by taking the reciprocal of the denominator. Then we factor and simplify.
$\displaystyle \frac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}=\frac{\frac{1}{x^{2}}-\frac{1}{y^{2}}}{\frac{1}{x}+\frac{1}{y}}=\frac{\frac{y^{2}}{x^{2}y^{2}}-\frac{x^2}{x^2y^2}}{\frac{y}{xy}+\frac{x}{xy}}=\frac{y^{2}-x^{2}}{x^{2}y^{2}}.\frac{xy}{y+x}=\frac{(y-x)(y+x)xy}{x^{2}y^{2}(y+x)}=\frac{y-x}{xy}$
