Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- x^{2} - 8 x - 5}{- 6 x^{2} - 5 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} - 8 x - 5}{- 6 x^{2} - 5 x + 9} = \lim_{x \to \infty}\frac{- 2 x - 8}{- 12 x - 5} = \lim_{x \to \infty}\frac{-2}{-12} = \frac{1}{6}