Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 112

\[\boxed{\mathbf{112}.}\]

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

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

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

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

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

\[D = 1 + 8 = 9\]

\[x_{1} = \frac{- 1 + 3}{4} = \frac{2}{4} = \frac{1}{2};\]

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

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

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

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

\[D_{1} = 4 - 3 = 1\]

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

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