<s>[INST] Show that $\frac{1}{a^n+b^n+c^n} = \frac{1}{a^n} + \frac{1}{b^n} + \frac{1}{c^n}$ Let $n \in N, n=2k+1, and \text{ } \frac{1}{a+b+c} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$.

Show that $$\frac{1}{a^n+b^n+c^n} = \frac{1}{a^n} + \frac{1}{b^n} + \frac{1}{c^n}$$

I have tried, but I don't get anything. Can you please give me a hint?
 [/INST] Hint 


*

*At the first step, show that $(a+b)(a+c)(b+c)=0$ 

*Next, show that two of the three numbers are opposite.

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