1. The problem is to calculate $3 \div \frac{17}{5}$ and express the answer in simplest form. 2. Recall the rule for dividing by a fraction: dividing by $\frac{a}{b}$ is the same as multiplying by its reciprocal $\frac{b}{a}$. 3. So, $3 \div \frac{17}{5} = 3 \times \frac{5}{17}$. 4. Multiply the numerators and denominators: $3 \times 5 = 15$ and denominator is $17$. 5. Thus, the expression becomes $\frac{15}{17}$. 6. Check if $\frac{15}{17}$ can be simplified further. Since 15 and 17 have no common factors other than 1, this is the simplest form. Final answer: $$\frac{15}{17}$$