1. The problem is to divide 3 by the fraction $\frac{17}{5}$. 2. Recall the rule for dividing by a fraction: $a \div \frac{b}{c} = a \times \frac{c}{b}$. 3. Applying this rule, we have: $$3 \div \frac{17}{5} = 3 \times \frac{5}{17}$$ 4. Multiply the numerators and denominators: $$= \frac{3 \times 5}{17} = \frac{15}{17}$$ 5. The fraction $\frac{15}{17}$ cannot be simplified further because 15 and 17 have no common factors other than 1. 6. Therefore, the final answer is: $$\frac{15}{17}$$