Сократите дробь: (6x^2-x-1)/(9x^2-1).

Ответ:

\[\frac{6x^{2} - x - 1}{9x^{2} - 1} =\]

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

\[6x^{2} - x - 1 =\]

\[= 6\left( x + \frac{1}{3} \right)\left( x - \frac{1}{2} \right) =\]

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

\[D = 1 + 24 = 25\]

\[x_{1} = \frac{1 + 5}{12} = \frac{6}{12} = \frac{1}{2};\ \]

\[x_{2} = \frac{1 - 5}{12} = - \frac{4}{12} = - \frac{1}{3}.\]