Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{2} - 7 x + 9}{5 x^{2} + 7 x + 7}

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} - 7 x + 9}{5 x^{2} + 7 x + 7} = \lim_{x \to -\infty}\frac{- 16 x - 7}{10 x + 7} = \lim_{x \to -\infty}\frac{-16}{10} = - \frac{8}{5}