\[\frac{4x^{2} - 11x - 3}{3 - x} = 0\]
\[ОДЗ:\ \ \ x \neq 3\]
\[4x² - 11x - 3 = 0\]
\[D = b^{2} - 4ac =\]
\[= 121 - 4 \cdot 4 \cdot ( - 3) =\]
\[= 121 + 48 = 169\]
\[x_{1} = \frac{11 + 13}{8} = \frac{24}{8} =\]
\[= 3\ (не\ подходит\ по\ ОДЗ)\]
\[x_{2} = \frac{11 - 13}{8} = - \frac{2}{8} = - \frac{1}{4}\]
\[Ответ:\ \ x = - \frac{1}{4}.\]