Решите уравнение: (x^3+6x^2-5x-30)/(x^2-36)=0.

Ответ:

\[\frac{x^{3} + 6x^{2} - 5x - 30}{x^{2} - 36} = 0\]

\[\frac{x^{2}(x + 6) - 5(x + 6)}{x^{2} - 36} = 0\]

\[\frac{\left( x^{2} - 5 \right)(x + 6)}{(x - 6)(x + 6)} = 0;\ \ \ \ \ x \neq \pm 6\]

\[\frac{x^{2} - 5}{x - 6} = 0\]

\[x^{2} - 5 = 0\]

\[x^{2} = 5\]

\[x = \pm \sqrt{5}.\]

\[Ответ:x = \pm \sqrt{5}.\]