Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{9 x^{2} - 9 x - 9}{4 x^{2} - 4 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{9 x^{2} - 9 x - 9}{4 x^{2} - 4 x + 9} = \lim_{x \to -\infty}\frac{18 x - 9}{8 x - 4} = \lim_{x \to -\infty}\frac{18}{8} = \frac{9}{4}