To solve the inequality

\[
x^2 - 1 > 0
\]

we start by analyzing where \( x^2 - 1 \) is greater than zero.

### Step 1: Rewrite the Inequality
Rewrite \( x^2 - 1 \) as a difference of squares:
\[
x^2 - 1 = (x - 1)(x + 1)
\]

So the inequality becomes:
\[
(x - 1)(x + 1) > 0
\]

### Step 2: Find the Critical Points
The critical points occur where \( (x - 1)(x + 1) = 0 \):
\[
x -

Explore how to solve the inequality x^2 - 1 > 0 using algebraic methods, including factorization with the difference of squares. This guide provides a step-by-step solution suitable for high school students in Grades 9-11.

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