1. **State the problem:** We need to eliminate the denominators in the equation $$\frac{2}{3} + 1 = \frac{3}{2}$$. 2. **Identify denominators:** The denominators are 3 and 2. 3. **Find common denominator:** The least common multiple (LCM) of 3 and 2 is 6. 4. **Multiply entire equation by 6:** $$6 \times \left(\frac{2}{3} + 1\right) = 6 \times \frac{3}{2}$$ 5. **Distribute multiplication:** $$6 \times \frac{2}{3} + 6 \times 1 = 6 \times \frac{3}{2}$$ 6. **Simplify each term:** $$2 \times 2 + 6 = 3 \times 3$$ $$4 + 6 = 9$$ 7. **Combine and verify:** $$10 = 9$$ which is false, showing the original equation is not true. **Final answer:** Multiplying both sides of the equation by the least common multiple of denominators (6) eliminates the fractions.