\[\frac{2}{y^{2} - 4} - \frac{1}{y^{2} + 2y} =\]
\[= \frac{2^{\backslash y}}{(y - 2)(y + 2)} - \frac{1^{\backslash y - 2}}{y(y + 2)} =\]
\[= \frac{2y - y + 2}{y(y - 2)(y + 2)} =\]
\[= \frac{y + 2}{y(y - 2)(y + 2)} = \frac{1}{y^{2} - 2y}.\]