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

Ответ:

\[2x² + 3x - 2 = 0\]

\[D = 9 + 16 = 25\]

\[x_{1} = \frac{- 3 + 5}{4} = \frac{2}{4} = \frac{1}{2};\ \ \]

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

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

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

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

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

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

\[D = 49 - 24 = 25\]

\[x_{1} = \frac{7 + 5}{4} = 3;\ \ \ x_{2} = \frac{7 - 5}{4} = \frac{1}{2}.\]

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

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

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