Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 2}\frac{5 x^{2} - 5 x - 10}{3 x^{2} - 4 x - 4}$

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: $LaTeX: \lim_{x \to 2}\frac{5 x^{2} - 5 x - 10}{3 x^{2} - 4 x - 4} = \lim_{x \to 2}\frac{10 x - 5}{6 x - 4} = \frac{10 (2) - 5}{6 (2) - 4} = \frac{15}{8}$