Answer
$\frac{x+2y}{4-x}$
Work Step by Step
Factor and simplify, we have:
$\frac{xz-xw+2yz-2yw}{z^2-w^2}\cdot\frac{4z+4w+xz+wx}{16-x^2}=\frac{x(z-w)+2y(z-w)}{(z+w)(z-w)}\cdot\frac{4(z+w)+x(z+w)}{(4+x)(4-x)}=\frac{(z-w)(x+2y)}{(z+w)(z-w)}\cdot\frac{(z+w)(4+x)}{(4+x)(4-x)}=\frac{(x+2y)}{1}\cdot\frac{1}{(4-x)}=\frac{x+2y}{4-x}$ where $z\pm w\ne0, x\ne \pm4$
