Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 8}\frac{3 x^{2} - 27 x + 24}{- 5 x^{2} + 49 x - 72}$

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: $LaTeX: \lim_{x \to 8}\frac{3 x^{2} - 27 x + 24}{- 5 x^{2} + 49 x - 72} = \lim_{x \to 8}\frac{6 x - 27}{49 - 10 x} = \frac{6 (8) - 27}{49 - 10 (8)} = - \frac{21}{31}$