College Algebra (11th Edition)

$\displaystyle \frac{y}{y+2}$
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: $\displaystyle =\frac{y}{y+2}$