Q: Let f:[0,infinity) be defined by f(x) = x^2/(x+1). Prove if it is uniformly continuous.

My solution: I let $\displaystyle \epsilon > 0, \delta > 0, x,y\epsilon[0,infinity)$ with $\displaystyle |x-y|<\delta$

then I have |f(x)-f(y)| = $\displaystyle |\frac{x^2}{x+1}-\frac{y^2}{y+1}| $ = $\displaystyle |\frac{x^2+x^2y-y^2x-y^2}{(x+1)(y+1)}|$

But I can't simpify it anymore to which would make the proof works...

Thank you.