Evaluate the limit $LaTeX: \displaystyle \lim_{x \to \infty}\frac{x^{2} - 4 x - 4}{6 x^{2} + 8 x - 6}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to \infty}\frac{x^{2} - 4 x - 4}{6 x^{2} + 8 x - 6} = \lim_{x \to \infty}\frac{2 x - 4}{12 x + 8} = \lim_{x \to \infty}\frac{2}{12} = \frac{1}{6}$