# How do you find the limit of  (3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1))  as x approaches infinity?

$\frac{3}{4}$
$\frac{3 {x}^{4} + 4}{\left({x}^{2} - 7\right) \left(4 {x}^{2} - 1\right)} = {x}^{4} / {x}^{4} \frac{3 + \frac{4}{x} ^ 4}{\left(1 - \frac{7}{x} ^ 2\right) \left(4 - \frac{1}{x} ^ 2\right)}$ so
${\lim}_{x \to \infty} \frac{3 {x}^{4} + 4}{\left({x}^{2} - 7\right) \left(4 {x}^{2} - 1\right)} = {\lim}_{x \to \infty} \frac{3 + \frac{4}{x} ^ 4}{\left(1 - \frac{7}{x} ^ 2\right) \left(4 - \frac{1}{x} ^ 2\right)} = \frac{3}{4}$