The given expression is:

\[
\frac{A^2 - 9}{2a - 6}
\]

### Step 1: Factor the numerator and denominator.
- The numerator \( A^2 - 9 \) is a difference of squares, which can be factored as:
  \[
  A^2 - 9 = (A - 3)(A + 3)
  \]
- The denominator \( 2a - 6 \) has a common factor of 2, so we factor it out:
  \[
  2a - 6 = 2(a - 3)
  \]

### Step 2: Simplify the expression.
Now the expression becomes:
\[
\frac{(A - 3)(A + 3)}{2(a - 3)}
\]

Since \( A - 3 \) appears in both the numerator and denominator, we can cancel it out (assuming \( A \neq 3 \) to avoid division by zero):

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

### Final Answer:
\[
\frac{A + 3}{2}
\]

Would you like more details on this process or have any questions?

Here are 5 related questions for practice:
1. How would you simplify \( \frac{x^2 - 16}{4x - 8} \)?
2. Can you factor \( x^2 - 25 \)?
3. What is the result of simplifying \( \frac{x^2 - y^2}{x - y} \)?
4. How do you solve \( \frac{(x + 2)(x - 2)}{2(x - 2)} \)?
5. What restrictions apply when canceling terms in rational expressions?

**Tip:** Always check for common factors in both the numerator and denominator before simplifying an expression.

Learn how to simplify the rational expression (A^2 - 9) / (2a - 6) by factoring the difference of squares and common factors. This detailed step-by-step solution is ideal for students in Grades 8-10 covering key algebraic concepts, such as factoring and simplifying rational expressions.

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