The given expression is:

\[
\frac{3}{x - 3} - \frac{x}{x^2 - 9}
\]

### Step-by-Step Solution

1. **Factor the denominator \( x^2 - 9 \):**
   The expression \( x^2 - 9 \) is a difference of squares, so it can be factored as:
   \[
   x^2 - 9 = (x - 3)(x + 3)
   \]

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

2. **Find a common denominator:**
   The least common denominator (LCD) between \( x - 3 \) and \( (x - 3)(x + 3) \) is \( (x - 3)(x + 3) \).

3. **Rewrite both terms with the common denominator:**
   The first term \( \frac{3}{x - 3} \) can be rewritten as:
   \[
   \frac{3}{x - 3} = \frac{3(x + 3)}{(x - 3)(x + 3)}
   \]
   
   Now the expression becomes:
   \[
   \frac{3(x + 3)}{(x - 3)(x + 3)} - \frac{x}{(x - 3)(x + 3)}
   \]

4. **Combine the terms:**
   Since both terms now have the same denominator, we can combine the numerators:
   \[
   \frac{3(x + 3) - x}{(x - 3)(x + 3)}
   \]

5. **Simplify the numerator:**
   Expand and simplify the numerator:
   \[
   3(x + 3) = 3x + 9
   \]
   So the numerator becomes:
   \[
   (3x + 9 - x) = 2x + 9
   \]

   Now the expression is:
   \[
   \frac{2x + 9}{(x - 3)(x + 3)}
   \]

### Final Answer:
\[
\frac{2x + 9}{(x - 3)(x + 3)}
\]

Would you like any further details or have questions?

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**Related Questions:**

1. How do you factor a difference of squares in general?
2. What are the steps to find the least common denominator in a rational expression?
3. How do you simplify complex rational expressions?
4. Can you explain how to handle undefined points in a rational function?
5. What is the domain of the simplified expression?

**Tip:** Always check for common factors between numerators and denominators before combining terms to simplify expressions.

Discover how to simplify the rational expression 3/(x - 3) - x/(x^2 - 9) by factoring the difference of squares and finding the least common denominator. This solution walks through key concepts in algebra, including factoring and rational expressions. Suitable for Grades 9-12.

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