Evaluate the limit LaTeX: \displaystyle \lim_{x \to 1}\frac{5 x^{2} + 15 x - 20}{8 x^{2} + x - 9}

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} + 15 x - 20}{8 x^{2} + x - 9} = \lim_{x \to 1}\frac{10 x + 15}{16 x + 1} = \frac{10 (1) + 15}{16 (1) + 1} = \frac{25}{17}