\[\frac{y + 6}{4y + 8} - \frac{y + 2}{4y - 8} + \frac{5}{y^{2} - 4} =\]
\[= \frac{y + 6^{\backslash y - 2}}{4 \cdot (y + 2)} - \frac{y + 2^{\backslash y + 2}}{4 \cdot (y - 2)} + \frac{5^{\backslash 4}}{(y - 2)(y + 2)} =\]
\[= \frac{(y + 6)(y - 2) - (y + 2)^{2} + 20}{4 \cdot (y + 2)(y - 2)} =\]
\[= \frac{y^{2} - 2y + 6y - 12 - y^{2} - 4y - 4 + 20}{4 \cdot (y + 2)(y - 2)} =\]
\[= \frac{4}{4 \cdot (y + 2)(y - 2)} = \frac{1}{y^{2} - 4}\]