Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{6 x^{2} + x - 6}{- 3 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{6 x^{2} + x - 6}{- 3 x^{2} - x - 6} = \lim_{x \to -\infty}\frac{12 x + 1}{- 6 x - 1} = \lim_{x \to -\infty}\frac{12}{-6} = -2