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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

Use l'Hôpital's Rule to evaluate \( \lim_{{x \to 1}} \frac{x + 1}{x^2 - 1} \). Then determine the limit using limit laws and commonly known limits.

This solution demonstrates how to evaluate the limit \( \lim_{{x \to 1}} \frac{x + 1}{x^2 - 1} \) using l'Hôpital's Rule and limit laws, covering essential calculus concepts such as indeterminate forms. Suitable for college calculus students.

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