Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 8 x^{2} - 9 x + 7}{- 6 x^{2} - 9 x - 8}

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} - 9 x + 7}{- 6 x^{2} - 9 x - 8} = \lim_{x \to \infty}\frac{- 16 x - 9}{- 12 x - 9} = \lim_{x \to \infty}\frac{-16}{-12} = \frac{4}{3}