How do you find the asymptotes for h(x)= (x^2-4)/(x)?

Jun 1, 2016

oblique asymptote y = x

Explanation:

The first step is to divide out.

$\Rightarrow \frac{{x}^{2} - 4}{x} = \left({x}^{2} / x - \frac{4}{x}\right) = x - \frac{4}{x}$

thus h(x) simplifies to $h \left(x\right) = x - \frac{4}{x}$

as $x \to \pm \infty , \frac{4}{x} \to 0 \text{ and } h \left(x\right) \to x$

$\Rightarrow y = x \text{ is the only asymptote}$
graph{(x^2-4)/x [-10, 10, -5, 5]}