Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -6}\frac{4 x^{2} + 28 x + 24}{x^{2} + 11 x + 30}$

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: $LaTeX: \lim_{x \to -6}\frac{4 x^{2} + 28 x + 24}{x^{2} + 11 x + 30} = \lim_{x \to -6}\frac{8 x + 28}{2 x + 11} = \frac{8 (-6) + 28}{2 (-6) + 11} = 20$