Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 5 x^{2} + 6 x + 8}{6 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{- 5 x^{2} + 6 x + 8}{6 x^{2} + 5 x - 6} = \lim_{x \to \infty}\frac{6 - 10 x}{12 x + 5} = \lim_{x \to \infty}\frac{-10}{12} = - \frac{5}{6}