\[\frac{y^{2} + 8y}{4 - y^{2}} - \frac{4y - 4}{4 - y^{2}} =\]
\[= \frac{y^{2} + 8y - 4y + 4}{4 - y^{2}} =\]
\[= \frac{y^{2} + 4y + 4}{(2 - y)(2 + y)} =\]
\[= \frac{(2 + y)²}{(2 - y)(2 + y)} = \frac{2 + y}{2 - y}\]