Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -3}\frac{3 x^{2} + 3 x - 18}{3 x^{2} + 4 x - 15}$

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: $LaTeX: \lim_{x \to -3}\frac{3 x^{2} + 3 x - 18}{3 x^{2} + 4 x - 15} = \lim_{x \to -3}\frac{6 x + 3}{6 x + 4} = \frac{6 (-3) + 3}{6 (-3) + 4} = \frac{15}{14}$