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!