1. **Problem a:** Simplify $15x \div 5xy$. 2. Write the division as a fraction: $$\frac{15x}{5xy}$$. 3. Factor numerator and denominator: $$\frac{15 \cdot x}{5 \cdot x \cdot y}$$. 4. Cancel common factors using \cancel{}: $$\frac{\cancel{15} \cdot \cancel{x}}{\cancel{5} \cdot \cancel{x} \cdot y} = \frac{3}{y}$$. 5. **Answer for a:** $\frac{3}{y}$. 6. **Problem b:** Simplify $\frac{12x^{2}y}{3x^{2}}$. 7. Factor numerator and denominator: $$\frac{12 \cdot x^{2} \cdot y}{3 \cdot x^{2}}$$. 8. Cancel common factors: $$\frac{\cancel{12} \cdot \cancel{x^{2}} \cdot y}{\cancel{3} \cdot \cancel{x^{2}}} = \frac{4y}{1} = 4y$$. 9. **Answer for b:** $4y$.