Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 8 x^{2} + 7 x + 9}{8 x^{2} + 3 x + 1}

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}{8 x^{2} + 3 x + 1} = \lim_{x \to -\infty}\frac{7 - 16 x}{16 x + 3} = \lim_{x \to -\infty}\frac{-16}{16} = -1