Hello there, I have this question about metrics, but the first part asks me to prove this horrible identity which I am having difficulty with. I would appreciate if somebody could point me in the right direction before I cover all my writing supplies with algebra.

Let $\displaystyle a,b,c$ be non-negative real numbers such that $\displaystyle a \le b+c$. Show that $\displaystyle \frac{b}{1+b} + \frac{c}{1+c} - \frac{a}{1+a} \ge 0 $.

Thanks again.