Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 5}\frac{3 x^{2} - 36 x + 105}{4 x^{2} - 15 x - 25}$

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: $LaTeX: \lim_{x \to 5}\frac{3 x^{2} - 36 x + 105}{4 x^{2} - 15 x - 25} = \lim_{x \to 5}\frac{6 x - 36}{8 x - 15} = \frac{6 (5) - 36}{8 (5) - 15} = - \frac{6}{25}$