Ukmt senior maths mentoring

Need help on this question (5b if you have the sheet):

Prove that for all positive real numbers, a,b and c that :

(a+b+c)/2
[is greater than or equal to]
(bc)/(b+c) + (ca)/(c+a) + (ab)/(a+b)

Have you tried anything?

I've tried taking the right from the left to hopefully be left with a positive remainder, but to make both of the denominators common and so on makes everything incredibly complicated which leads me to believe that it's not the best route to go

I've also considered drawing geometrical representations of each of the fractions but so far, nothing's coming to mind...