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

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

\[= \frac{(5x - 1)(x + 4)}{(5x - 1)(5x + 1)} = \frac{x + 4}{5x + 1}\]

\[5x^{2} + 19x - 4 =\]

\[= 5\left( x - \frac{1}{5} \right)(x + 4) =\]

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

\[D = 361 + 80 = 441 = 21^{2}\]

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

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