Решите уравнение: (4a^3+8a^2-3a-6)/(a^2-4)=0.

\[\frac{4a^{3} + 8a^{2} - 3a - 6}{a^{2} - 4} = 0\]

\[a^{2} - 4 \neq 0\]

\[a^{2} \neq 4\]

\[a \neq \pm 2.\]

\[4a^{3} + 8a^{2} - 3a - 6 = 0\]

\[4a^{2}(a + 2) - 3(a + 2) = 0\]

\[(a + 2)\left( 4a^{2} - 3 \right) = 0\]

\[a + 2 = 0\]

\[a = - 2\ (не\ подходит).\]

\[4a^{2} - 3 = 0\]

\[4a^{2} = 3\]

\[a^{2} = \frac{3}{4}\]

\[a = \pm \frac{\sqrt{3}}{2}.\]

\[Ответ:a = \pm \frac{\sqrt{3}}{2}.\]