Сократить дробь: (4x^2-5x+1)/(x^2+5x-6).

Ответ:

\[\frac{4x^{2} - 5x + 1}{x^{2} + 5x - 6} =\]

\[= \frac{(4x - 1)(x - 1)}{(x + 6)(x - 1)} = \frac{4x - 1}{x + 6}.\]

\[1)\ 4x^{2} - 5x + 1 =\]

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

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

\[D = 25 - 16 = 9\]

\[x_{1} = \frac{5 + 3}{8} = 1;\]

\[x_{2} = \frac{5 - 3}{8} = \frac{2}{8} = \frac{1}{4}.\]

\[2)\ x^{2} + 5x - 6 = (x + 6)(x - 1)\]

\[x_{1} + x_{2} = - 5;\ \ x_{1} \cdot x_{2} = - 6\]

\[x_{1} = - 6;\ \ \ x_{2} = 1.\]