Answer
$(x-y)(x+y)$
or
$x^{2}-y^{2}$
Work Step by Step
Factor what we can:
$x^{2}-y^{2}$ = difference of squares = $(x-y)(x+y)$
$x^{2}+xy$ = $x(x+y)$
Rewrite the problem:
$\displaystyle \frac{(x-y)(x+y)}{x}\cdot\frac{x(x+y)}{(x+y)}=\qquad$ ... reduce common factors
=$\displaystyle \frac{(x-y)(x+y)}{(1)}\cdot\frac{(1)(1)}{(1)}=$
=$(x-y)(x+y)$
or
$x^{2}-y^{2}$
