Evaluate the limit LaTeX: \displaystyle \lim_{x \to 3}\frac{2 x^{2} - 22 x + 48}{3 x^{2} - x - 24}

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{2 x^{2} - 22 x + 48}{3 x^{2} - x - 24} = \lim_{x \to 3}\frac{4 x - 22}{6 x - 1} = \frac{4 (3) - 22}{6 (3) - 1} = - \frac{10}{17}