Evaluate the limit $LaTeX: \displaystyle \lim_{x \to 1}\frac{5 x^{2} - 25 x + 20}{- 4 x^{2} + 9 x - 5}$

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: $LaTeX: \lim_{x \to 1}\frac{5 x^{2} - 25 x + 20}{- 4 x^{2} + 9 x - 5} = \lim_{x \to 1}\frac{10 x - 25}{9 - 8 x} = \frac{10 (1) - 25}{9 - 8 (1)} = -15$