При каких а значение дроби (a^3+108-3a^2-36a)/(a^2-9) равно нулю?

\[\frac{a^{3} + 108 - 3a^{2} - 36a}{a^{2} - 9} = 0\]

\[\frac{a^{2}(a - 3) - 36 \cdot (a - 3)}{a^{2} - 9} = 0\]

\[\frac{(a - 3)\left( a^{2} - 36 \right)}{(a - 3)(a + 3)} = 0;\ \ \ \ \ \ a \neq \pm 3\]

\[\frac{a^{2} - 36}{a + 3} = 0\]

\[a^{2} - 36 = 0\]

\[a^{2} = 36\]

\[a = \pm 6.\]

\[Ответ:при\ a = \pm 6.\]