Сократите дробь: (3x^2+2x-1)/(7x-3x^2-2).

Ответ:

\[3x^{2} + 2x - 1 = 0\]

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

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

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

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

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

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

\[7x - 3x^{2} - 2 = 0\]

\[3x^{2} - 7x + 2 = 0\]

\[x_{1} + x_{2} = \frac{7}{3}\]

\[x_{1} \cdot x_{2} = \frac{2}{3}\]

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

\[7x - 3x^{2} - 2 =\]

\[= - 3 \cdot (x - 2)\left( x - \frac{1}{3} \right) =\]

\[= (2 - x)(3x - 1).\]