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

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 + 4}{- 2 x^{2} - 2 x - 3} = \lim_{x \to -\infty}\frac{- 18 x - 9}{- 4 x - 2} = \lim_{x \to -\infty}\frac{-18}{-4} = \frac{9}{2}