1. **State the problem:** Simplify the expression $$\frac{x^2 + 2x + 1}{x + 3}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor the numerator and denominator if possible, then cancel common factors. 3. **Factor the numerator:** $$x^2 + 2x + 1 = (x + 1)^2$$ because it is a perfect square trinomial. 4. **Rewrite the expression:** $$\frac{(x + 1)^2}{x + 3}$$. 5. **Check for common factors:** The denominator is $x + 3$, which is different from $x + 1$, so no factors cancel. 6. **Final simplified form:** $$\frac{(x + 1)^2}{x + 3}$$. This is the simplest form unless you perform polynomial division for a different expression form.