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

Answer:

Refer to explanation

Explanation:

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

and as $x \to 2$ , $\frac{x}{{x}^{2} + x - 6} \to \infty$ and

$x \to - 3$ , $\frac{x}{{x}^{2} + x - 6} \to \infty$

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