The expression provided is:

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

We can simplify this fraction by factoring the denominator. Notice that the denominator $x^2 + 2x + 1$ is a perfect square trinomial:

$x^2 + 2x + 1 = (x+1)^2$

Thus, the expression becomes:

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

We can simplify further by canceling one $x+1$ term from the numerator and denominator, assuming $x \neq -1$ (because at $x = -1$, the expression would be undefined):

$\frac{1}{x+1}, \quad \text{for} \ x \neq -1$

So, the simplified expression is:

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

Would you like further clarification or details on any part of this solution?

Here are 5 related questions for you:

1. How do you factor quadratic expressions like $x^2 + 2x + 1$?
2. What happens if $x = -1$ in the original expression?
3. How do you simplify rational expressions?
4. Can you explain the difference between undefined and zero in expressions like this?
5. What if the denominator were not a perfect square trinomial?

Tip: Always check for factoring opportunities in both the numerator and denominator before simplifying rational expressions.