How to prove this inequality?

Submitted by TommyR on Thu, 08/23/2007 - 20:40.

For $a_1,a_2,a_3,a_4,a_5,a_6>0$ prove that:

$\frac{a_1}{a_2+a_3}+\frac{a_2}{a_3+a_4}+\frac{a_3}{a_4+a_5}+<br /> \frac{a_4}{a_5+a_6}+\frac{a_5}{a_6+a_1}+\frac{a_6}{a_1+a_2}\geq3$