https://file.aiquickdraw.com/mathbot/file/1726947681890zvz7gwzi.jpg

The expression you've provided is:

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

### Step 1: Factor both the numerator and denominator.

- **Numerator** \( x^2 - x - 2 \) can be factored as:
  \[
  x^2 - x - 2 = (x - 2)(x + 1)
  \]

- **Denominator** \( x^2 - 1 \) is a difference of squares:
  \[
  x^2 - 1 = (x - 1)(x + 1)
  \]

### Step 2: Rewrite the expression using the factored forms.

\[
\frac{(x - 2)(x + 1)}{(x - 1)(x + 1)}
\]

### Step 3: Simplify the expression by canceling out common factors.
The factor \( (x + 1) \) appears in both the numerator and denominator, so we cancel it out:

\[
\frac{x - 2}{x - 1}
\]

### Final Answer:
The simplified form of the given expression is:

\[
\frac{x - 2}{x - 1}
\]

Do you have any further questions or would you like additional details?

Here are 5 related questions you might explore:
1. How do you factor a quadratic expression?
2. What is the difference of squares and how is it factored?
3. Can this expression be simplified further if certain values of \( x \) are given?
4. Are there any restrictions on \( x \) in this simplified expression?
5. How does factoring help in solving rational equations?

**Tip:** Always check for common factors when simplifying rational expressions to avoid unnecessary complexity.

Simplify the expression \(\frac{x^2 - x - 2}{x^2 - 1}\).

Learn how to simplify the rational expression \(\frac{x^2 - x - 2}{x^2 - 1}\) using factoring techniques and the difference of squares. This problem is suitable for students in Grades 8-10 and covers important algebraic concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation