Use Giant 1s to create a common denominator of $xy$.

$\frac{1}{x}\Big(\frac{y}{y}\Big)-\frac{1}{y}\Big(\frac{x}{x}\Big)$

Rewrite the first factor using your answer to part (a).

$=\left(\frac{y-x}{xy}\right)\frac{(x+y)}{1}$

Multiply numerator by numerator and denominator by denominator.

$\large =\frac{xy+y^2-x^2-xy}{xy}=\frac{y^2-x^2}{xy}$