# AIME 2015 Problem 8

Algebra Level 5

Let $$a$$ and $$b$$ be positive integers satisfying $$\dfrac{ab+1}{a+b} < \frac{3}{2}$$. The maximum possible value of $$\dfrac{a^3b^3+1}{a^3+b^3}$$ is $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are relatively prime positive integers. Find $$p+q$$.

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