\[\frac{1}{16 - 2a} + \frac{a^{2}}{a^{3} - 64a} =\]
\[= \frac{1^{\backslash a(a + 8)}}{- 2(a - 8)} + \frac{{a^{2}}^{\backslash\text{-}2}}{a(a - 8)(a + 8)} =\]
\[= \frac{a^{2} + 8a - 2a^{2}}{- 2a(a - 8)(a + 8)} =\]
\[= \frac{- a(a - 8)}{- 2a(a - 8)(a + 8)} = \frac{1}{2a + 16}.\]