Answer
$\frac{x^{2}(y-1)}{y^{2}(x-1)}$
Work Step by Step
We multiply by $xy$, distribute and simplify:
$\displaystyle \frac{x-\frac{x}{y}}{y-\frac{y}{x}}=\frac{xy(x-\frac{x}{y})}{xy(y-\frac{y}{x})}=\frac{x^{2}y-x^{2}}{xy^{2}-y^{2}}=\frac{x^{2}(y-1)}{y^{2}(x-1)}$
