Evaluate the limit LaTeX: \displaystyle \lim_{x \to -\infty}\frac{6 x^{2} + 6 x + 3}{- 9 x^{2} - 4 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{6 x^{2} + 6 x + 3}{- 9 x^{2} - 4 x + 3} = \lim_{x \to -\infty}\frac{12 x + 6}{- 18 x - 4} = \lim_{x \to -\infty}\frac{12}{-18} = - \frac{2}{3}