To simplify the expression \(\frac{3x - 9}{x^2 - 9}\), follow these steps:

1. **Factor the numerator and the denominator**:
   - The numerator \(3x - 9\) can be factored as \(3(x - 3)\).
   - The denominator \(x^2 - 9\) is a difference of squares, which can be factored as \((x - 3)(x + 3)\).

So the expression becomes:
\[
\frac{3(x - 3)}{(x - 3)(x + 3)}
\]

2. **Cancel out the common factor**:
   - The \((x - 3)\) terms in the numerator and denominator cancel out, leaving:
\[
\frac{3}{x + 3}
\]

Thus, the simplified form of the expression is:
\[
\frac{3}{x + 3}
\]
(Note: This simplification is valid as long as \(x \neq 3\), to avoid division by zero.)

Would you like more details on this solution?

### Related Questions:
1. What is the domain of the simplified function \(\frac{3}{x+3}\)?
2. How would the process change if the denominator was \(x^2 + 9\) instead of \(x^2 - 9\)?
3. Can you simplify similar expressions like \(\frac{4x - 12}{x^2 - 16}\)?
4. How can you verify the solution graphically or by substitution?
5. What are some other examples of the difference of squares in algebra?

### Tip:
Always check for common factors before canceling terms to simplify fractions efficiently.

Learn how to simplify the rational expression (3x-9)/(x^2-9) step-by-step by factoring and using the difference of squares. Understand the concepts of rational expressions and the cancellation property of fractions. Suitable for students in Grades 8-10.

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