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

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to -\infty}\frac{6 x^{2} - 6 x - 2}{3 x^{2} - 2 x - 3} = \lim_{x \to -\infty}\frac{12 x - 6}{6 x - 2} = \lim_{x \to -\infty}\frac{12}{6} = 2$