Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{5 x^{2} + 5 x - 30}{8 x^{2} + 28 x + 12}$

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: $LaTeX: \lim_{x \to -3}\frac{5 x^{2} + 5 x - 30}{8 x^{2} + 28 x + 12} = \lim_{x \to -3}\frac{10 x + 5}{16 x + 28} = \frac{10 (-3) + 5}{16 (-3) + 28} = \frac{5}{4}$