# What is the limit of (x^2-4)/(2x-4x^2) as x goes to infinity?

${\lim}_{x \to \infty} \frac{{x}^{2} - 4}{2 x - 4 {x}^{2}} = {\lim}_{x \to \infty} {x}^{2} \frac{1 - \frac{4}{x} ^ 2}{{x}^{2} \left(\frac{2}{x} - 4\right)} = \frac{1 - {\lim}_{x \to \infty} \frac{4}{x} ^ 2}{{\lim}_{x \to \infty} \frac{2}{x} - 4} = \frac{1 - 0}{0 - 4} = - \frac{1}{4}$