Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 6 x^{2} + 9 x + 8}{4 x^{2} - 2 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{- 6 x^{2} + 9 x + 8}{4 x^{2} - 2 x - 7} = \lim_{x \to \infty}\frac{9 - 12 x}{8 x - 2} = \lim_{x \to \infty}\frac{-12}{8} = - \frac{3}{2}