The given expression appears to be:

$\frac{x^2 + 2x + 1}{x + 1}$

Step-by-Step Simplification:

1. Factorize the numerator $x^2 + 2x + 1$: $x^2 + 2x + 1 = (x + 1)(x + 1) = (x + 1)^2$

2. Write the expression with the factorized numerator: $\frac{(x + 1)^2}{x + 1}$

3. Simplify by canceling one $x + 1$ term (provided $x + 1 \neq 0$): $\frac{(x + 1)^2}{x + 1} = x + 1$

Final Answer:

x + 1 \quad \text{(for x \neq -1)}

Let me know if you'd like further clarifications or more examples related to this concept!

Here are 5 related questions to expand understanding:

1. What happens if $x = -1$ in the given expression?
2. How do you handle a similar simplification when the numerator cannot be factored?
3. What is the general process for simplifying rational expressions?
4. How does factoring work for other quadratic expressions, like $x^2 - 4x + 4$?
5. What happens when the numerator degree is smaller than the denominator?

Tip: Always check for restrictions on the variable (like $x \neq -1$ here) when simplifying rational expressions!