Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 1}\frac{4 x^{2} - 28 x + 24}{- 6 x^{2} - x + 7}$

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: $LaTeX: \lim_{x \to 1}\frac{4 x^{2} - 28 x + 24}{- 6 x^{2} - x + 7} = \lim_{x \to 1}\frac{8 x - 28}{- 12 x - 1} = \frac{8 (1) - 28}{- 12 (1) - 1} = \frac{20}{13}$