Решите уравнение: (3x^2+11x-4)/(3x-1).

\[\frac{3x^{2} + 11x - 4}{3x - 1}\]

\[ОДЗ:\ \ \ 3x - 1 \neq 0\]

\[\ \Longrightarrow x \neq \frac{1}{3}\]

\[3x^{2} + 11x - 4 - 3 \cdot (3x - 1) =\]

\[= 0\]

\[3x^{2} + 11x - 4 - 9x + 3 = 0\]

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

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

\[= 4 - 4 \cdot 3 \cdot ( - 1) = 4 + 12 = 16\]

\[x_{1} = \frac{- 2 + 4}{6} = \frac{2}{6} =\]

\[= \frac{1}{3}\ (не\ подходит\ по\ ОДЗ)\]

\[x_{2} = \frac{- 2 - 4}{6} = - \frac{6}{6} = - 1\]

\[Ответ:x = - 1.\]