Answer
$\text{The given complex fraction simplifies to } \dfrac{y-2}{y+2}$.
Work Step by Step
$\displaystyle \begin{array}{ l l }
=\dfrac{y\left( 2-\dfrac{2}{y}\right)}{y\left( 2+\dfrac{2}{y}\right)} & \begin{array}{{>{\displaystyle}l}}
\mathrm{Multiply\ the\ numerator\ and\ denominator\ }\\
\mathrm{of\ the\ complex\ fraction\ by} \ y \text{(the LCD of all the fractions.)}
\end{array}\\
& \\
=\dfrac{y-y\left(\dfrac{2}{y}\right)}{y+y\left(\dfrac{2}{y}\right)} & \mathrm{Apply\ the\ distributive\ property.}\\
& \\
=\dfrac{y-\dfrac{2y}{y}}{y+\dfrac{2y}{y}} & \mathrm{Multiply} \ y\ \mathrm{by} \ \dfrac{2}{y}.\\
& \\
=\dfrac{y-2\cdot \dfrac{y}{y}}{y+2\cdot \dfrac{y}{y}} & \mathrm{Apply\ the\ rule} \ \dfrac{ab}{c} =a\left(\dfrac{b}{c}\right).\\
& \\
=\dfrac{y-2}{y+2} & \mathrm{Apply\ the\ rule} \ \dfrac{a}{a} =1.
\end{array}$
