Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{4 x^{2} + 8 x - 60}{- 9 x^{2} + 24 x + 9}$

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: $LaTeX: \lim_{x \to 3}\frac{4 x^{2} + 8 x - 60}{- 9 x^{2} + 24 x + 9} = \lim_{x \to 3}\frac{8 x + 8}{24 - 18 x} = \frac{8 (3) + 8}{24 - 18 (3)} = - \frac{16}{15}$