I have been working on this for a little bit now, but I can't get it.

$\displaystyle \mbox{If } a \leq b + c \mbox{ and } a,b,c \geq 0, \mbox{ show } \frac{a}{a+1} \leq \frac{b}{b+1} + \frac{c}{c+1}$. Its the very first question in a series of questions on metric spaces, so I have a feeling I am missing something obvious. Thank you.