1. **State the problem:** We need to find an expression for the area of a rectangle with height $\frac{3}{n+2}$ and width $\frac{5(n+2)}{13n}$. 2. **Formula for area of a rectangle:** The area $A$ is given by $$A = \text{height} \times \text{width}$$ 3. **Substitute the given expressions:** $$A = \frac{3}{n+2} \times \frac{5(n+2)}{13n}$$ 4. **Simplify the expression:** Since $n+2$ appears in both numerator and denominator, they cancel out: $$A = \frac{3}{\cancel{n+2}} \times \frac{5\cancel{(n+2)}}{13n} = \frac{3 \times 5}{13n} = \frac{15}{13n}$$ 5. **Final answer:** The simplest form of the area is $$\boxed{\frac{15}{13n}}$$ This expression gives the area of the rectangle in terms of $n$.