Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{3 x^{2} - 12 x + 9}{- 3 x^{2} + 11 x - 6}$

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: $LaTeX: \lim_{x \to 3}\frac{3 x^{2} - 12 x + 9}{- 3 x^{2} + 11 x - 6} = \lim_{x \to 3}\frac{6 x - 12}{11 - 6 x} = \frac{6 (3) - 12}{11 - 6 (3)} = - \frac{6}{7}$