Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{- 6 x^{2} - 9 x - 1}{x^{2} + 7 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 - 1}{x^{2} + 7 x - 7} = \lim_{x \to \infty}\frac{- 12 x - 9}{2 x + 7} = \lim_{x \to \infty}\frac{-12}{2} = -6