`(12^2-4^2)/(9^2-3^2)` =?

Answer

To solve the expression \((12^2 - 4^2) / (9^2 - 3^2)\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\).

### Step-by-Step Solution:

1. **Identify the squares in the numerator and denominator**:
- The numerator is \(12^2 - 4^2\).
- The denominator is \(9^2 - 3^2\).

2. **Apply the difference of squares formula to the numerator**:
\[ 12^2 - 4^2 = (12 - 4)(12 + 4) \]
- Calculate \(12 - 4 = 8\) and \(12 + 4 = 16\).
- So, the numerator becomes:
\[ 8 \times 16 \]

3. **Apply the difference of squares formula to the denominator**:
\[ 9^2 - 3^2 = (9 - 3)(9 + 3) \]
- Calculate \(9 - 3 = 6\) and \(9 + 3 = 12\).
- So, the denominator becomes:
\[ 6 \times 12 \]

4. **Rewrite the expression**:
\[ \frac{12^2 - 4^2}{9^2 - 3^2} = \frac{8 \times 16}{6 \times 12} \]

5. **Simplify the fraction**:
- First, calculate \(8 \times 16 = 128\) and \(6 \times 12 = 72\).
- So, we have:
\[ \frac{128}{72} \]

6. **Reduce the fraction**:
- Find the greatest common divisor (GCD) of 128 and 72, which is 8.
- Divide both the numerator and the denominator by 8:
\[ \frac{128 \div 8}{72 \div 8} = \frac{16}{9} \]

7. **Final answer**:
\[ \frac{12^2 - 4^2}{9^2 - 3^2} = \frac{16}{9} \]