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

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{- 2 x^{2} - 6 x + 2}{5 x^{2} + 3 x - 9} = \lim_{x \to \infty}\frac{- 4 x - 6}{10 x + 3} = \lim_{x \to \infty}\frac{-4}{10} = - \frac{2}{5}