Powers of aa

Algebra Level 3

If aa2+1=13\dfrac{a}{a^2+1}= \dfrac{1}{3}, determine

a3a6+a5+a4+a3+a2+a+1\large \frac{a^3}{a^6 + a^5 + a^4 + a^3 + a^2 + a + 1}

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