Uniform Continuity of f(x) = 1/(|x|+1) on R: Epsilon-Delta Proof

[PsychonautQQ]

Homework Statement

Prove that f(x) = 1/(|x|+1) is uniformly continuous on R.

Homework Equations

The Attempt at a Solution

This needs to be an e-d proof (epsilon-delta).

So I suppose we should start with let e>0, then we want to find a d such that for all x,y in R, if |x-y|<d then |f(x)-f(y)|<e.

I'm having trouble locating a d that will work, is there some algebra trick or other type of trick that can help me?

 

[PsychonautQQ]

bump because i don't want 666 post count