1. **State the problem:** Simplify the expression $\frac{2x + 2}{2}$. 2. **Formula and rules:** When dividing a sum by a number, you can divide each term separately by that number: $$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$$ 3. **Apply the rule:** $$\frac{2x + 2}{2} = \frac{2x}{2} + \frac{2}{2}$$ 4. **Simplify each term:** $$\frac{2x}{2} = x$$ $$\frac{2}{2} = 1$$ 5. **Final simplified expression:** $$x + 1$$ This means the original expression simplifies to $x + 1$.