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

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 + 7}{- 7 x^{2} + x + 2} = \lim_{x \to \infty}\frac{- 12 x - 9}{1 - 14 x} = \lim_{x \to \infty}\frac{-12}{-14} = \frac{6}{7}