Can a Metric Space be Constructed from the Inequality a <= b + c?

[pdonovan]

Homework Statement

Show:
if a <= b + c,
then a/(a + 1) <= (b / (b + 1)) + (c / (c + 1))

I'm really not sure where to start from the initial statement a <= b + c. I'm using this in order to show that the metric space e(a,b) = d(a,b)/(1+d(a,b)) exists. Any help would be greatly appreciated, thank you!

 

[pdonovan]

Also, this is for all a,b,c >= 0.