Сократите дробь: (3p^2-7p-6)/(4-9p^2).

Ответ:

\[\frac{3p^{2} - 7p - 6}{4 - 9p^{2}} =\]

\[= \frac{(3p + 1)(p - 3)}{(2 - 3p)(2 + 3p)} = \frac{p - 3}{2 - 3p}.\]

\[3p^{2} - 7p - 6 =\]

\[= 3\left( p + \frac{2}{3} \right)(p - 3) =\]

\[= (3p + 2)(p - 3)\]

\[D = 49 + 72 = 121\]

\[p_{1} = \frac{7 + 11}{\mathbf{6}} = 3;\]

\[p_{2} = \frac{7 - 11}{\mathbf{6}} = - \frac{4}{6} = - \frac{2}{3}.\]