Answer
$\displaystyle \frac{4(x+y)}{3(x-y)}$
Work Step by Step
Factor what we can:
$x^{2}+2xy+y^{2}$ = (square of a sum) = $(x+y)^{2}$
$x^{2}-2xy+y^{2}$ = (square of a difference) = $(x-y)^{2}$
$4x-4y$ = $4(x-y)$
$3x+3y=3(x+y)$
Rewrite the problem:
$\displaystyle \frac{(x+y)(x+y)}{(x-y)(x-y)}\cdot\frac{4(x-y)}{3(x+y)}=\qquad$ ... reduce common factors
=$\displaystyle \frac{(1)(x+y)}{(1)(x-y)}\cdot\frac{4(1)}{3(1)}=$
=$\displaystyle \frac{4(x+y)}{3(x-y)}$
