How prove this inequality $\sum\limits_{cyc}\frac{1}{(ka+(k+1)b+(k+2)c)^2}\le \frac{1}{(k+1)^2(ab+bc+ac)}$

Question

Inequality:

Let $a,b,c\ge 0$. and $k\ge\dfrac{\sqrt{21}-3}{3}$ show that $$\sum_{cyc}\dfrac{1}{(ka+(k+1)b+(k+2)c)^2}\le \dfrac{1}{(k+1)^2(ab+bc+ac)}$$

This problem is from:

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=52&t=501921

I want use this link methods,But I failed.maybe someone can use this methods to prove it.

Thank you