Решите уравнение: (3x^2-5x-2)/(2-x)=0.

Ответ:

\[\frac{3x^{2} - 5x - 2}{2 - x} = 0\]

\[ОДЗ:\ \ 2 - x \neq 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \Longrightarrow x \neq 2\]

\[3x^{2} - 5x - 2 = 0\]

\[D = b^{2} - 4ac =\]

\[= 25 - 4 \cdot 3 \cdot ( - 2) =\]

\[= 25 + 24 = 49\]

\[x_{1} = \frac{5 + 7}{6} = \frac{12}{6} =\]

\[= 2\ (не\ подходит\ по\ ОДЗ)\]

\[x_{2} = \frac{5 - 7}{6} = - \frac{2}{6} = - \frac{1}{3}.\]

\[Ответ:x = - \frac{1}{3}.\]