Why is there no vertical asymptote on

Question

F(x) = x/(x^2+1)

What i learned is that to find vertical asymptote you have to set the denominator To 0 and solve for x ?
In that case I find that x=-1,1

Answer 1

vertical asymptotes occur when you try to divide by zero.

x^2+1 is never zero.

You solved for x^2-1 = 0

Answer 2

I don't get it ?

Answer 3

huh? huh? How can you say that?

x^2 is always positive, right? At least it is never negative.

So, x^2+1 is always positive, and always at least 1.

So, dividing by x^2+1 will never yield a vertical asymptote.

Answer 4

Yesss okay thank you sir