Answer
$-xy$
Work Step by Step
We form a common denominator for both fractions and add them. Then we switch division to multiplication by taking the reciprocal of the bottom fraction. Finally we simplify:
$\displaystyle \frac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{x^2}-\frac{1}{y^2}}=\frac{\frac{x^{2}-y^{2}}{xy}}{\frac{y^{2}-x^{2}}{x^{2}y^{2}}}=\frac{x^{2}-y^{2}}{xy}*\frac{x^{2}y^{2}}{y^{2}-x^{2}}=\frac{xy}{-1}=-xy$
