Сократите дробь: (12x^2+x-1)/(9x^2+6x+1).

Ответ:

\[\frac{12x^{2} + x - 1}{9x^{2} + 6x + 1} =\]

\[= \frac{(3x + 1)(4x - 1)}{(3x + 1)^{2}} = \frac{4x - 1}{3x + 1}.\]

\[12x^{2} + x - 1 =\]

\[= 12\left( x + \frac{1}{3} \right)\left( x - \frac{1}{4} \right) =\]

\[= (3x + 1)(4x - 1)\]

\[D = 1 + 48 = 49\]

\[x_{1} = \frac{- 1 + 7}{24} = \frac{6}{24} = \frac{1}{4};\]

\[x_{2} = \frac{- 1 - 7}{24} = - \frac{8}{24} = - \frac{1}{3}.\]