Сократите дробь: (4x^2-7x-2)/(11x-4x^2+3).

Ответ:

\[D = 49 + 32 = 81\]

\[x_{1} = \frac{7 + 9}{8} = \frac{16}{8} = 2;\ \ \ \]

\[x_{2} = \frac{7 - 9}{8} = - \frac{2}{8} = - \frac{1}{4}.\]

\[4x^{2} - 7x - 2 =\]

\[= 4 \cdot (x - 2)\left( x + \frac{1}{4} \right) =\]

\[= (x - 2)(4x + 1)\]

\[4x^{2} - 11x - 3 = 0\]

\[D = 121 + 48 = 169\]

\[x_{1} = \frac{11 + 13}{8} = \frac{24}{8} = 3;\ \ \ \]

\[x_{2} = \frac{11 - 13}{8} = - \frac{2}{8} = - \frac{1}{4}.\]

\[- 4x^{2} + 11x + 3 =\]

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

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