Сократите дробь: (12x^2-x-1)/(16x^2+8x+1).

Ответ:

\[\frac{12x^{2} - x - 1}{16x^{2} + 8x + 1} =\]

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

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

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

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

\[D = 1 + 48 = 49\]

\[x_{1} = \frac{1 + 7}{24} = \frac{8}{24} = \frac{1}{3};\]

\[x_{2} = \frac{1 - 7}{24} = - \frac{6}{24} = - \frac{1}{4}.\]