Сократите дробь (3p^2+p-2)/(4-9p^2).

Ответ:

\[\frac{3p^{2} + p - 2}{4 - 9p^{2}} = - \frac{(3p - 2)(p + 1)}{(3p - 2)(3p + 2)} =\]

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

\[3p^{2} + p - 2 = 3 \cdot \left( p - \frac{2}{3} \right)(p + 1) =\]

\[= (3p - 2)(p + 1)\]

\[D = 1 + 24 = 25\]

\[p_{1} = \frac{- 1 + 5}{6} = \frac{4}{6} = \frac{2}{3};\ \ \ \ \ \]

\[p_{2} = \frac{- 1 - 5}{6} = - 1.\]