Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 4}\frac{2 x^{2} - 20 x + 48}{- 6 x^{2} + 30 x - 24}$

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: $LaTeX: \lim_{x \to 4}\frac{2 x^{2} - 20 x + 48}{- 6 x^{2} + 30 x - 24} = \lim_{x \to 4}\frac{4 x - 20}{30 - 12 x} = \frac{4 (4) - 20}{30 - 12 (4)} = \frac{2}{9}$