1. **State the problem:** Simplify the expression $$\frac{x^2 + 2x + 1}{x + 1}$$. 2. **Recall the formula and rules:** The numerator is a quadratic expression. We can try to factor it to simplify the division. 3. **Factor the numerator:** Notice that $$x^2 + 2x + 1$$ is a perfect square trinomial. $$x^2 + 2x + 1 = (x + 1)^2$$ 4. **Rewrite the expression:** $$\frac{(x + 1)^2}{x + 1}$$ 5. **Simplify by canceling common factors:** $$\frac{\cancel{(x + 1)}(x + 1)}{\cancel{(x + 1)}} = x + 1$$ 6. **Final answer:** $$x + 1$$ This simplification is valid for all $$x \neq -1$$ because division by zero is undefined.