What's the best way to compute $\frac{a^4 + b^4 + c^4}{a^2 + b^2 + c^2}$ So, my teacher gave us this to compute yesterday, and I'm completly confused on how should I proceed : 
$$\frac{1^4 + 2012^4 +2013^4}{1^2 + 2012^2 + 2013^2}$$
I've tried several ways, but most of them are very long, for example I've simplified both numbers :
$2012^2 = (2 * 10^3)^2 + 12^2 + 24 * 10^3$ 
$2013^2 = (2 * 10^3)^2 + 13^2 + 26 * 10^3$
I can't see how this could help me solve this problem . So how how should I go with this kind of problems in general ?

Hint:
$$\frac{1^4+x^4+(x+1)^4}{1^2+x^2+(x+1)^2}=x^2+x+1$$
