Problem 2 : Basic Operations

Algebra Level 5

A positive real number is given. In each move, we can either add \(3\) to it, subtract \(3\) to it, multiply it by \(3\) and divide it by \(3\). The sum of all numbers such that after exactly \(3\) moves, the original number comes back is \(\frac{a}{b}\), where \(a\) and \(b\) are relatively prime positive integers. Find \(a + b\).

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