Сократите дробь (4c^2+7c-2)/(1-16c^2).

Ответ:

\[\frac{4c^{2} + 7c - 2}{1 - 16c^{2}} = - \frac{(4c - 1)(c + 2)}{(4c - 1)(4c + 1)} =\]

\[= - \frac{c + 2}{4c + 1}\]

\[4c^{2} + 7c - 2 = 4\left( c - \frac{1}{4} \right)(c + 2) =\]

\[= (4c - 1)(c + 2)\]

\[D = 49 + 32 = 81\]

\[c_{1} = \frac{- 7 + 9}{8} = \frac{2}{8} = \frac{1}{4};\ \ \ \ \]

\[c_{2} = \frac{- 7 - 9}{8} = - 2.\]