How do I prove the following inequality? How do I proceed to solve the inequality  $$\frac{(a^2+b^2)}{(a+b)} + \frac {(b^2+c^2)}{(b+c)} + \frac{(a^2+c^2)}{(a+c)} \geq (a+b+c)$$  where $a , b , c > 0$
I have thought of taking the terms on the $LHS$ and converting them to $AM$ and then use the $AM-GM$ theorem , but I cant figure out how to convert $\frac {(a^2+b^2)}{(a+b)}$ to $AM$.I have tried finding $a_1$ and $a_2$ by doing 
$ (\frac{(a_1+a_2)}{2}\bigr)^2 \geq$ $\frac{(a^2+b^2)}{(a+b)}$

If $a$, $b$, $c>0$ then
$$\frac{a^2+b^2}{a+b}\ge\frac{a+b}2$$
etc.
