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