Сократите дробь: (x^3+x^2-72x)/(9x-72).

Ответ:

\[\frac{x^{3} + x^{2} - 72x}{9x - 72} =\]

\[= \frac{x\left( x^{2} + x - 72 \right)}{9(x - 8)} =\]

\[= \frac{x(x + 9)(x - 8)}{9(x - 8)} = \frac{x(x + 9)}{9}\]

\[x^{2} + x - 72 = 0\]

\[x_{1} + x_{2} = - 1;\ \ \ \ x_{1} \cdot x_{2} = - 72\]

\[x_{1} = - 9;\ \ \ x_{2} = 8.\]