Given $a+b+c=0$, simplify the following. I am here again to ask a question about an exercise I saw around but i'm having a lot of trouble with. I know the answer is 3abc, but as in many of my questions, I am interested in the why and how.
Given $a+b+c=0$, simplify:
$$\frac{(a^3-abc)^3+(c^3-abc)^3+(b^3-abc)^3}{(c^2-ab)(b^2-ac)(a^2-bc)}$$

Your idea that $a^3+b^3+c^3=3abc$ is a good one. 
Consider your numerator $x^3+y^3+z^3$, where $x = a^3-abc$ and so forth, try to see what $x+y+z$ is, and what the relationship between $x^3+y^3+z^3$ and $3xyz$ is.
