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