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The given limit problem is:

\[
\lim_{{x \to 1}} \frac{{x^2 - 1}}{{x - 1}}
\]

To solve this, notice that the expression \( x^2 - 1 \) is a difference of squares, which can be factored as:

\[
x^2 - 1 = (x - 1)(x + 1)
\]

Substitute this into the original limit expression:

\[
\lim_{{x \to 1}} \frac{{(x - 1)(x + 1)}}{{x - 1}}
\]

For \( x \neq 1 \), we can cancel out the \( (x - 1) \) terms:

\[
\lim_{{x \to 1}} (x + 1)
\]

Now, substitute \( x = 1 \):

\[
1 + 1 = 2
\]

Thus, the value of the limit is:

\[
\boxed{2}
\]

Would you like more details or further clarifications?

Here are 5 related questions to expand on this concept:
1. What happens when direct substitution into a limit results in an indeterminate form?
2. How can factoring help in solving limits with rational expressions?
3. What is the difference between a removable discontinuity and a non-removable one?
4. How do you handle limits at infinity?
5. What is L'Hopital's rule and when is it applied?

**Tip**: When you encounter an indeterminate form like \(\frac{0}{0}\), try factoring, rationalizing, or using L'Hopital's Rule to resolve it.

lim (x^2 - 1) / (x - 1) as x approaches 1

Learn how to solve the limit lim (x^2 - 1) / (x - 1) as x approaches 1 by factoring the expression. This step-by-step solution involves algebraic concepts like factoring and handling indeterminate forms. Suitable for students in Grades 10-12.

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