Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{4 x^{2} + 6 x - 8}{5 x^{2} - 5 x - 1}

The limit is an indeterminate form of the type LaTeX: \displaystyle \frac{\infty}{\infty} . Using L'Hospitial's rule 2 times gives: LaTeX: \lim_{x \to \infty}\frac{4 x^{2} + 6 x - 8}{5 x^{2} - 5 x - 1} = \lim_{x \to \infty}\frac{8 x + 6}{10 x - 5} = \lim_{x \to \infty}\frac{8}{10} = \frac{4}{5}