Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 4}\frac{3 x^{2} - 21 x + 36}{8 x^{2} - 26 x - 24}$

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: $LaTeX: \lim_{x \to 4}\frac{3 x^{2} - 21 x + 36}{8 x^{2} - 26 x - 24} = \lim_{x \to 4}\frac{6 x - 21}{16 x - 26} = \frac{6 (4) - 21}{16 (4) - 26} = \frac{3}{38}$