Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- x^{2} - 6 x + 8}{9 x^{2} - 4 x + 4}

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} - 6 x + 8}{9 x^{2} - 4 x + 4} = \lim_{x \to -\infty}\frac{- 2 x - 6}{18 x - 4} = \lim_{x \to -\infty}\frac{-2}{18} = - \frac{1}{9}