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The given expression is:

\[
\frac{x^2 - x - 6}{x^2 - 9}
\]

We need to simplify this expression.

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

#### Numerator: \(x^2 - x - 6\)
We are looking for two numbers that multiply to \(-6\) and add up to \(-1\). These numbers are \(-3\) and \(2\). So, the factored form of the numerator is:

\[
x^2 - x - 6 = (x - 3)(x + 2)
\]

#### Denominator: \(x^2 - 9\)
This is a difference of squares, and it factors as:

\[
x^2 - 9 = (x - 3)(x + 3)
\]

### Step 2: Write the expression in factored form.

\[
\frac{(x - 3)(x + 2)}{(x - 3)(x + 3)}
\]

### Step 3: Cancel the common factor \((x - 3)\).

As long as \(x \neq 3\), we can cancel the common factor:

\[
\frac{x + 2}{x + 3}
\]

### Final Simplified Expression:
\[
\frac{x + 2}{x + 3}
\]

So, the correct answer is **A**.

---

Would you like further explanation on any part of this process? Here are 5 related questions to consider:

1. What is the method for factoring quadratic expressions?
2. How do you identify the difference of squares?
3. Why is it important to check for restrictions on \(x\) when simplifying rational expressions?
4. How would this change if we added another term to the expression?
5. What is the process for simplifying more complex rational expressions?

**Tip**: Always check for common factors that can be canceled when simplifying rational expressions!

Randy wrote the following expression. What is the expression written in simplest terms? (x^2 - x - 6) / (x^2 - 9)

Learn how to simplify the rational expression (x^2 - x - 6) / (x^2 - 9) by factoring both the numerator and denominator. This problem involves factoring quadratics and recognizing the difference of squares. Suitable for students in Grades 8-10.

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