Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- x^{2} + 3 x - 2}{2 x^{2} - 9 x - 9}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to -\infty}\frac{- x^{2} + 3 x - 2}{2 x^{2} - 9 x - 9} = \lim_{x \to -\infty}\frac{3 - 2 x}{4 x - 9} = \lim_{x \to -\infty}\frac{-2}{4} = - \frac{1}{2}