Сократить дробь: (3x^2+5x-2)/(x^2-3x-10).

Ответ:

\[\frac{3x^{2} + 5x - 2}{x^{2} - 3x - 10} = \frac{(3x - 1)(x + 2)}{(x + 2)(x - 5)} =\]

\[= \frac{3x - 1}{x - 5}.\]

\[1)\ 3x^{2} + 5x - 2 =\]

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

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

\[D = 25 + 24 = 49\]

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

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

\[2)\ x^{2} - 3x - 10 = (x + 2)(x - 5)\]

\[x_{1} + x_{2} = 3;\ \ x_{1} \cdot x_{2} = - 10\]

\[x_{1} = 5;\ \ \ x_{2} = - 2.\]