Сократите дробь: (2x^2-x-1)/(x^2-1).

Ответ:

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

\[= \frac{2x + 1}{x + 1}.\]

\[2x^{2} - x - 1 =\]

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

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

\[D = 1 + 8 = 9\]

\[x_{1} = \frac{1 + 3}{4} = 1;\]

\[x_{2} = \frac{1 - 3}{4} = - \frac{2}{4} = - \frac{1}{2}.\]