Reducing $\frac{a^n(b-c) - b^n(a-c) + c^n(a-b)}{(a-b)(a-c)(b-c)}$ for $n>2$ 
Simplify
$$\frac{a^n(b-c) - b^n(a-c) + c^n(a-b)}{(a-b)(a-c)(b-c)}$$ for $n>2$.

The answer is $(a+b+c)^n$, but I can't seen to get it.
Can someone help me?
Thanks

$$\frac{(b-c)\times a^n - (a-c)\times b^n + (a-b)\times c^n}{(a-b)(a-c)(b-c)}=$$
$$\frac{a^n-b^n+c^n}{1}=$$
$$\boxed{\frac{a^n}{(a - b) (a - c)} - \frac{b^n}{(a - b) (b - c)} + \frac{c^n}{(a - c) (b - c)}}.$$
