# How do you find the horizontal asymptote for F(x)=(x^2+x-12) / (x^2-4)?

Feb 28, 2016

see explanantion

#### Explanation:

As $x$ becomes very large the remaining elements have less and less influence.

We end up with$\text{ } {x}^{2} / {x}^{2} = 1$

${\lim}_{x \to \infty} \frac{{x}^{2} + x - 12}{{x}^{2} - 4} = {x}^{2} / {x}^{2} = + 1$

${\lim}_{x \to - \infty} \frac{{x}^{2} + x - 12}{{x}^{2} - 4} = {x}^{2} / {x}^{2} = + 1$