Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$ I'm stuck at this algebra problem, it seems to me that's what's provided doesn't even at all.
Provided:  $$a+b+c=0$$
Find the value of:  $$\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$$
Like I'm not sure where to start, and the provided clue doesn't even make sense.  There's no way I can think of to factor this big polynomial into a form like $a\times p+b\times q+c\times r=s$ where $p,q,r,s\in\mathbb{Z}$.
Thanks!

$$ −a^2b−b^2c−c^2a+a^2c+b^2a+c^2b  
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  
\\ 
\overset{\tiny{+abc-abc}}{=} 
\Big[ abc+bc^2-b^2c-ac^2 \Big] 
+ 
\Big[ -a^2b-abc+ab^2+a^2c \Big] 
\\ 
=c(ab+bc-b^2-ac)-a(ab+bc-b^2-ac) 
\\ 
=(c-a)(ab+bc-b^2-ac) 
\\ 
=(c-a)(a-b)(b-c) 
. $$
