$\frac{\frac{xy-y^2}{1+xy}-xy}{\frac{x^2-xy}{1+xy}-x^2}$
$=(\frac{xy-y^2}{1+xy}-xy):(\frac{x^2-xy}{1+xy}-x^2)$
$=(\frac{xy-y^2-xy(1+xy)}{1+xy}):(\frac{x^2-xy-x^2(1+xy)}{1+xy})$
$=\frac{xy-y^2-xy-x^2y^2}{1+xy}:\frac{x^2-xy-x^2-x^3y}{1+xy}$
$=\frac{-y^2-x^2y^2}{1+xy}:\frac{-xy-x^3y}{1+xy}$
$=\frac{-y^2(1+x^2)}{1+xy}.\frac{1+xy}{-xy(1+x^2)}$
$=\frac{-y^2}{-xy}$
$=\frac{y}{x}$
