Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{- 6 x^{2} + 3 x - 8}{- 2 x^{2} - 9 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{- 6 x^{2} + 3 x - 8}{- 2 x^{2} - 9 x + 5} = \lim_{x \to -\infty}\frac{3 - 12 x}{- 4 x - 9} = \lim_{x \to -\infty}\frac{-12}{-4} = 3