Answer
$-xy$
Work Step by Step
Looking at the denominator:
Find the LCD (i.e. $x^{2}y^{2}$) and adjust accordingly:
$=\frac{y^{2}}{x^{2}y^{2}}-\frac{x^{2}}{x^{2}y^{2}}$
$=\frac{y^{2}-x^{2}}{x^{2}y^{2}}$
Looking at the numerator:
Find the LCD (i.e. $xy$) and adjust accordingly:
$=\frac{x^{2}}{xy}-\frac{y^{2}}{xy}$
$=\frac{x^{2}-y^{2}}{xy}$
This then becomes:
$=\frac{\frac{x^{2}-y^{2}}{xy}}{\frac{y^{2}-x^{2}}{x^{2}y^{2}}}$
Divide the fractions:
$=\frac{x^{2}-y^{2}}{xy}\times\frac{x^{2}y^{2}}{y^{2}-x^{2}}$
$=\frac{(x^{2}-y^{2})\times x^{2}y^{2}}{xy\times(y^{2}-x^{2})}$
$=-\frac{(x^{2}-y^{2})\times x^{2}y^{2}}{xy\times(x^{2}-y^{2})}$
Cancel out the common factors:
$=-\frac{x^{2}y^{2}}{xy}$
$=-xy$
