Answer
$\dfrac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}=\dfrac{y-x}{xy}$
Work Step by Step
$\dfrac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}$
Rewrite the fraction like this:
$\dfrac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}=\dfrac{\dfrac{1}{x^{2}}-\dfrac{1}{y^{2}}}{\dfrac{1}{x}+\dfrac{1}{y}}=...$
Evaluate the substraction in the numerator and the sum in the denominator
$...=\dfrac{\dfrac{y^{2}-x^{2}}{x^{2}y^{2}}}{\dfrac{y+x}{xy}}=...$
Evaluate the division:
$...=\dfrac{xy(y^{2}-x^{2})}{x^{2}y^{2}(y+x)}=...$
Simplify:
$...=\dfrac{y^{2}-x^{2}}{xy(y+x)}=\dfrac{(y-x)(y+x)}{xy(y+x)}=\dfrac{y-x}{xy}$
