\[\frac{y + 6^{\backslash y + 6}}{y - 6} - \frac{y + 2^{\backslash y - 6}}{y + 6} =\]
\[= \frac{y^{2} + 12y + 36 - \left( y^{2} + 2y - 6y - 12 \right)}{(y - 6)(y + 6)} =\]
\[= \frac{y^{2} + 12y + 36 - y^{2} + 4y + 12}{y^{2} - 36} =\]
\[= \frac{16y + 48}{y^{2} - 36}.\]