Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{3 x^{2} + 33 x + 72}{4 x^{2} + 17 x + 15}$

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: $LaTeX: \lim_{x \to -3}\frac{3 x^{2} + 33 x + 72}{4 x^{2} + 17 x + 15} = \lim_{x \to -3}\frac{6 x + 33}{8 x + 17} = \frac{6 (-3) + 33}{8 (-3) + 17} = - \frac{15}{7}$