1. **State the problem:** Simplify the expression $$\frac{9(v+2)}{5v} \times \frac{2}{v+2}$$ as a single fraction in simplest form. 2. **Write the multiplication of fractions:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{9(v+2)}{5v} \times \frac{2}{v+2} = \frac{9(v+2) \times 2}{5v \times (v+2)}$$ 3. **Simplify the numerator and denominator:** $$= \frac{18(v+2)}{5v(v+2)}$$ 4. **Cancel common factors:** The factor $(v+2)$ appears in both numerator and denominator, so we can cancel it: $$= \frac{18\cancel{(v+2)}}{5v\cancel{(v+2)}}$$ 5. **Final simplified fraction:** $$= \frac{18}{5v}$$ **Answer:** The expression simplifies to $$\frac{18}{5v}$$.