Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -8}\frac{4 x^{2} - 4 x - 288}{- 4 x^{2} - 26 x + 48}$

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: $LaTeX: \lim_{x \to -8}\frac{4 x^{2} - 4 x - 288}{- 4 x^{2} - 26 x + 48} = \lim_{x \to -8}\frac{8 x - 4}{- 8 x - 26} = \frac{8 (-8) - 4}{- 8 (-8) - 26} = - \frac{34}{19}$