Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 3 x^{2} + 5 x - 1}{2 x^{2} - x - 2}

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{- 3 x^{2} + 5 x - 1}{2 x^{2} - x - 2} = \lim_{x \to -\infty}\frac{5 - 6 x}{4 x - 1} = \lim_{x \to -\infty}\frac{-6}{4} = - \frac{3}{2}