Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{3 x^{2} - 3 x - 6}{6 x^{2} - 3 x - 18}$

The limit is an indeterminate form of the type $LaTeX: \displaystyle \frac{0}{0}$ . Using L'Hospitial's rule and then the evaluation theorem gives: $LaTeX: \lim_{x \to 2}\frac{3 x^{2} - 3 x - 6}{6 x^{2} - 3 x - 18} = \lim_{x \to 2}\frac{6 x - 3}{12 x - 3} = \frac{6 (2) - 3}{12 (2) - 3} = \frac{3}{7}$