Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{3 x^{2} + 12 x - 63}{- 2 x^{2} - x + 21}$

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: $LaTeX: \lim_{x \to 3}\frac{3 x^{2} + 12 x - 63}{- 2 x^{2} - x + 21} = \lim_{x \to 3}\frac{6 x + 12}{- 4 x - 1} = \frac{6 (3) + 12}{- 4 (3) - 1} = - \frac{30}{13}$