Сократите дробь (5a^2+19a-4)/(1-25a^2).

Ответ:

\[\frac{5a^{2} + 19a - 4}{1 - 25a^{2}} = - \frac{(5a - 1)(a + 4)}{(5a - 1)(5a + 1)} =\]

\[= - \frac{a + 4}{5a + 1}\]

\[5a^{2} + 19a - 4 = 5 \cdot \left( a - \frac{1}{5} \right)(a + 4) =\]

\[= (5a - 1)(a + 4)\]

\[D = 361 + 80 = 441\]

\[a_{1} = \frac{- 19 + 21}{10} = \frac{2}{10} = \frac{1}{5};\ \ \ \ \ \]

\[a_{2} = \frac{- 19 - 21}{10} = - 4.\]