Сократить дробь: (2x^2+11x-6)/(-3x^2-x^3+18x).

Ответ:

\[\frac{2x^{2} + 11x - 6}{- 3x^{2} - x^{3} + 18x} =\]

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

\[2)\ 2x^{2} + 11x - 6 =\]

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

\[= (2x - 1)(x + 6)\]

\[D = 121 + 48 = 169\]

\[x_{1} = \frac{( - 11 + 13)}{4} = \frac{1}{2};\]

\[x_{2} = \frac{- 11 - 13}{4} = - 6.\]

\[2) - 3x^{2} - x^{3} + 18x =\]

\[= - x\left( x^{2} + 3x - 18 \right) =\]

\[= - x(x + 6)(x - 3)\]

\[x_{1} + x_{2} = - 3;\ \ x_{1} \cdot x_{2} = - 18\]

\[x_{1} = - 6;\ \ \ x_{2} = 3.\]