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