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

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{9 x^{2} + 9 x - 5}{5 x^{2} - x - 6} = \lim_{x \to -\infty}\frac{18 x + 9}{10 x - 1} = \lim_{x \to -\infty}\frac{18}{10} = \frac{9}{5}