Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{9 x^{2} + 6 x - 1}{7 x^{2} + 7 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} + 6 x - 1}{7 x^{2} + 7 x + 6} = \lim_{x \to -\infty}\frac{18 x + 6}{14 x + 7} = \lim_{x \to -\infty}\frac{18}{14} = \frac{9}{7}