Evaluate the limit LaTeX: \displaystyle \lim_{x \to \infty}\frac{9 x^{2} + 8 x + 9}{6 x^{2} - 8 x + 3}

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{9 x^{2} + 8 x + 9}{6 x^{2} - 8 x + 3} = \lim_{x \to \infty}\frac{18 x + 8}{12 x - 8} = \lim_{x \to \infty}\frac{18}{12} = \frac{3}{2}