Answer
$\displaystyle \frac{y}{y+2}$
Work Step by Step
We simplify:
$\displaystyle \frac{y-2}{y-\frac{4}{y}}$
Multiply through by $y$:
$\displaystyle =\frac{y(y-2)}{y(y-\frac{4}{y})}$
Distribute:
$\displaystyle =\frac{y^{2}-2y}{y^{2}-4}$
Factor out $y$ from the top and the bottom using $(a+b)(a-b)=a^2-b^2$:
$\displaystyle =\frac{y(y-2)}{(y+2)(y-2)}$
Simplify:
$\displaystyle =\frac{y}{y+2}$
