Evaluate the limit $LaTeX: \displaystyle \lim_{x \to \infty}\frac{6 x^{2} + 2 x - 4}{- 2 x^{2} - 6 x + 9}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{\infty}{\infty}$ . Using L'Hospitial's rule 2 times gives: $LaTeX: \lim_{x \to \infty}\frac{6 x^{2} + 2 x - 4}{- 2 x^{2} - 6 x + 9} = \lim_{x \to \infty}\frac{12 x + 2}{- 4 x - 6} = \lim_{x \to \infty}\frac{12}{-4} = -3$