Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 6 x^{2} + 8 x + 1}{5 x^{2} - 5 x - 6}

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{- 6 x^{2} + 8 x + 1}{5 x^{2} - 5 x - 6} = \lim_{x \to -\infty}\frac{8 - 12 x}{10 x - 5} = \lim_{x \to -\infty}\frac{-12}{10} = - \frac{6}{5}