1. **State the problem:** Simplify the expression $\frac{x}{3} + \frac{x-1}{2}$. 2. **Find a common denominator:** The denominators are 3 and 2. The least common denominator (LCD) is 6. 3. **Rewrite each fraction with the LCD:** $$\frac{x}{3} = \frac{x \times 2}{3 \times 2} = \frac{2x}{6}$$ $$\frac{x-1}{2} = \frac{(x-1) \times 3}{2 \times 3} = \frac{3(x-1)}{6}$$ 4. **Add the fractions:** $$\frac{2x}{6} + \frac{3(x-1)}{6} = \frac{2x + 3(x-1)}{6}$$ 5. **Simplify the numerator:** $$2x + 3(x-1) = 2x + 3x - 3 = 5x - 3$$ 6. **Final simplified expression:** $$\frac{5x - 3}{6}$$ This is the simplified form of the original expression.