Problem 2 : Basic Operations

Algebra Level 4

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 $a + b$ .