Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{5 x^{2} - 55 x + 120}{- 4 x^{2} + 8 x + 12}$

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: $LaTeX: \lim_{x \to 3}\frac{5 x^{2} - 55 x + 120}{- 4 x^{2} + 8 x + 12} = \lim_{x \to 3}\frac{10 x - 55}{8 - 8 x} = \frac{10 (3) - 55}{8 - 8 (3)} = \frac{25}{16}$