To solve the limit:

$\lim_{{x \to 1}} \frac{x + 1}{x^2 - 1}$

using L'Hôpital's Rule, we start by confirming that the limit yields an indeterminate form of $\frac{0}{0}$ when we substitute $x = 1$:

Step 1: Substitute $x = 1$

• Numerator: $x + 1 = 1 + 1 = 2$.
• Denominator: $x^2 - 1 = 1^2 - 1 = 0$.

Since only the denominator is zero, we don't actually need L'Hôpital's Rule here. This is a straightforward case where we can directly calculate