What are the asymptotes for $\frac{x}{x^{2} + x - 6}$ $x/(x^2+x-6)$ ?

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Answer 1 · 2015-09-21T02:18:20

Refer to explanation

We see that as $x \to \pm \infty$ $x->+-oo$ , $\frac{x}{x^{2} + x - 6} \to 0$ $x/(x^2+x-6)->0$ hence $y = 0$ $y=0$ horizontal asymptote.

and as $x \to 2$ $x->2$ , $\frac{x}{x^{2} + x - 6} \to \infty$ $x/(x^2+x-6)->oo$ and

$x \to - 3$ $x->-3$ , $\frac{x}{x^{2} + x - 6} \to \infty$ $x/(x^2+x-6)->oo$

so vertical asymptote are $x = 2, x = - 3$ $x=2,x=-3$

What are the asymptotes for x/(x^2+x-6)xx2+x−6x/(x^2+x-6)?