Evaluate the limit $LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 9 x^{2} + 9 x + 1}{3 x^{2} + 6 x - 5}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to \infty}\frac{- 9 x^{2} + 9 x + 1}{3 x^{2} + 6 x - 5} = \lim_{x \to \infty}\frac{9 - 18 x}{6 x + 6} = \lim_{x \to \infty}\frac{-18}{6} = -3$