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R=∑x=1∞x5−9xx8−3x6+27x2−81\large\mathfrak R=\displaystyle\sum_{x=1}^{\infty}\dfrac{x^5-9x}{x^8-3x^6+27x^2-81}R=x=1∑∞x8−3x6+27x2−81x5−9x
If R\mathfrak RR can be written in the form pq\dfrac pqqp, where ppp and qqq are coprime positive integers, find ∣p−q∣|p-q|∣p−q∣.
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