Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{3 x^{2} + 3 x - 36}{6 x^{2} - 26 x + 24}$

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: $LaTeX: \lim_{x \to 3}\frac{3 x^{2} + 3 x - 36}{6 x^{2} - 26 x + 24} = \lim_{x \to 3}\frac{6 x + 3}{12 x - 26} = \frac{6 (3) + 3}{12 (3) - 26} = \frac{21}{10}$