Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 4}\frac{4 x^{2} + 20 x - 144}{- 8 x^{2} + 26 x + 24}$

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: $LaTeX: \lim_{x \to 4}\frac{4 x^{2} + 20 x - 144}{- 8 x^{2} + 26 x + 24} = \lim_{x \to 4}\frac{8 x + 20}{26 - 16 x} = \frac{8 (4) + 20}{26 - 16 (4)} = - \frac{26}{19}$