Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{2} + 8 x - 6}{- 9 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{- 8 x^{2} + 8 x - 6}{- 9 x^{2} - 5 x + 6} = \lim_{x \to -\infty}\frac{8 - 16 x}{- 18 x - 5} = \lim_{x \to -\infty}\frac{-16}{-18} = \frac{8}{9}