Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -\infty}\frac{6 x^{2} - 6 x - 8}{6 x^{2} - 6 x + 6}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to -\infty}\frac{6 x^{2} - 6 x - 8}{6 x^{2} - 6 x + 6} = \lim_{x \to -\infty}\frac{12 x - 6}{12 x - 6} = \lim_{x \to -\infty}\frac{12}{12} = 1$