Final Answer
Step-by-step Solution
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The trinomial $x^2+2x+1$ is a perfect square trinomial, because it's discriminant is equal to zero
Using the perfect square trinomial formula
Factoring the perfect square trinomial
Simplify the fraction $\frac{\left(x+1\right)^{2}}{x+1}$ by $x+1$
Evaluate the limit $\lim_{x\to-1}\left(x+1\right)$ by replacing all occurrences of $x$ by $-1$
Subtract the values $1$ and $-1$