Question

(y-2/y+2  +  y+2/y-2)    : 2y²+8/y²+4y+4

Answer 1

((y-2)²+(y+2)²)/((y-2)(y+2))·(y+2)²/(2y²+8)=(2y²+8)/((y-2)(y+2))·(y+2)²/(2y²+8)=(y+2)/(y-2)

Answer 2

$( frac{y-2}{y+2} + frac{y+2}{y-2}): frac{2 y^{2}+8 }{y^2+4y+4}= frac{(y-2)(y-2)+(y+2)(y+2)}{(y+2)(y-2)}* frac{ y^{2}+4y+4 }{2y^2+8} = \ \ = frac{2y^2+8}{(y+2)(y-2)}* frac{(y+2)(y+2)}{2y^2+8} = frac{y+2}{y-2}$