Evaluate the limit LaTeX: \displaystyle \lim_{x \to 3}\frac{5 x^{2} - 55 x + 120}{- 7 x^{2} + 14 x + 21}

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 3}\frac{5 x^{2} - 55 x + 120}{- 7 x^{2} + 14 x + 21} = \lim_{x \to 3}\frac{10 x - 55}{14 - 14 x} = \frac{10 (3) - 55}{14 - 14 (3)} = \frac{25}{28}