It looks like you're simplifying an expression, but it seems like the last part might be a little bit off. Let's go through the steps carefully:

Given:

• Numerator: $x^2 - 9$
• Denominator: $x^2 - x - 6$

Step 1: Factor the numerator

The numerator is a difference of squares: $x^2 - 9 = (x - 3)(x + 3)$

Step 2: Factor the denominator

To factor $x^2 - x - 6$, we need two numbers that multiply to $-6$ and add to $-1$. These numbers are $-3$ and $2$, so: $x^2 - x - 6 = (x - 3)(x + 2)$

Step 3: Simplify the expression

Now the expression looks like: $\frac{(x - 3)(x + 3)}{(x - 3)(x + 2)}$ We can cancel out the common factor of $(x - 3)$ (but remember that $x \neq 3$ because division by zero is undefined): $\frac{x + 3}{x + 2}$

Step 4: Identify the restrictions

The restrictions come from the factors in the denominator. Since $(x - 3)$ and $(x + 2)$ cannot be zero, the restrictions are: $x \neq 3 \quad \text{and} \quad x \neq -2$

Final Answer:

The simplified expression is: $\frac{x + 3}{x + 2}$ with restrictions: $x \neq 3, \quad x \neq -2$

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Would you like more details about any of the steps, or do you have any further questions? Here's a list of related questions to explore:

1. How do we factor quadratic expressions when the leading coefficient is not 1?
2. What is the difference between a difference of squares and a sum/difference of cubes?
3. Can we cancel terms in rational expressions only when they are factors of both the numerator and denominator?
4. How do you find the restrictions on a rational expression?
5. What happens when you try to simplify a rational expression with a zero denominator?

Tip: Always check for restrictions by considering what values would make any denominator equal to zero, as division by zero is undefined.