Evaluate the limit $LaTeX: \displaystyle \lim_{x \to -8}\frac{4 x^{2} + 8 x - 192}{- 3 x^{2} - 23 x + 8}$

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: $LaTeX: \lim_{x \to -8}\frac{4 x^{2} + 8 x - 192}{- 3 x^{2} - 23 x + 8} = \lim_{x \to -8}\frac{8 x + 8}{- 6 x - 23} = \frac{8 (-8) + 8}{- 6 (-8) - 23} = - \frac{56}{25}$