Question 8
Let $a$ and $b$ be positive integers satisfying $\frac{ab + 1}{a + b} \lt \frac{3}{2}.$ The maximum possible value of $\frac{a^3 b^3 + 1}{a^3 + b^3}$ is $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$