Evaluate the limit LaTeX: \displaystyle \lim_{x \to 5}\frac{3 x^{2} - 18 x + 15}{9 x^{2} - 37 x - 40}

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 5}\frac{3 x^{2} - 18 x + 15}{9 x^{2} - 37 x - 40} = \lim_{x \to 5}\frac{6 x - 18}{18 x - 37} = \frac{6 (5) - 18}{18 (5) - 37} = \frac{12}{53}