# An algebra problem by Abhay Kumar

Algebra Level 5

$\dfrac{(a^3+b^3+c^3)^2 (a^4+b^4+c^4)}{(a^5+b^5+c^5)^2}$

Given $a, b$ and $c$ satisfy $a + b + c = 0$ and $a^5 + b^5 + c^5 \neq 0$, the value of the above expression can be expressed as $\dfrac mn$, where $m$ and $n$ are coprime positive integers, calculate the value of $m+n$.

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