MK-MO 2014 Problem 4

Let $a,b,c$ be real numbers such that $a+b+c = 4$ and $a,b,c > 1$ . Prove that:

$$\frac 1{a-1} + \frac 1{b-1} + \frac 1{c-1} \ge \frac 8{a+b} + \frac 8{b+c} + \frac 8{c+a}$$