Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 5 x^{2} - 2 x - 9}{8 x^{2} + 6 x + 3}

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} - 2 x - 9}{8 x^{2} + 6 x + 3} = \lim_{x \to \infty}\frac{- 10 x - 2}{16 x + 6} = \lim_{x \to \infty}\frac{-10}{16} = - \frac{5}{8}