Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 3}\frac{5 x^{2} - 50 x + 105}{5 x^{2} - 7 x - 24}$

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: $LaTeX: \lim_{x \to 3}\frac{5 x^{2} - 50 x + 105}{5 x^{2} - 7 x - 24} = \lim_{x \to 3}\frac{10 x - 50}{10 x - 7} = \frac{10 (3) - 50}{10 (3) - 7} = - \frac{20}{23}$