Сократить дробь: (3x^2+5x-2)/(x^2-4).

Ответ:

\[\frac{3x^{2} + 5x - 2}{x^{2} - 4} =\]

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

\[3x^{2} + 5x - 2 =\]

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

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

\[D = 25 + 24 = 49\]

\[x_{1} = \frac{- 5 + 7}{6} = \frac{2}{6} = \frac{1}{3};\ \]

\[x_{2} = \frac{- 5 - 7}{6} = - \frac{12}{6} = - 2.\]