Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{5 x^{2} + 5 x - 60}{- 4 x^{2} + 15 x - 9}$

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: $LaTeX: \lim_{x \to 3}\frac{5 x^{2} + 5 x - 60}{- 4 x^{2} + 15 x - 9} = \lim_{x \to 3}\frac{10 x + 5}{15 - 8 x} = \frac{10 (3) + 5}{15 - 8 (3)} = - \frac{35}{9}$