Find the value of :
`((18.5)^(2) - (6.5)^(2))/(18.5 + 6.5)`

Answer

To solve the expression \(\frac{(18.5)^2 - (6.5)^2}{18.5 + 6.5}\), 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 \(a\) and \(b\)**:
- Let \(a = 18.5\) and \(b = 6.5\).

2. **Apply the difference of squares formula**:
- According to the formula, we can rewrite the numerator:
\[ (18.5)^2 - (6.5)^2 = (18.5 + 6.5)(18.5 - 6.5) \]

3. **Calculate \(18.5 + 6.5\)**:
- \(18.5 + 6.5 = 25\).

4. **Calculate \(18.5 - 6.5\)**:
- \(18.5 - 6.5 = 12\).

5. **Substitute back into the expression**:
- Now we can substitute these values back into the expression:
\[ \frac{(18.5 + 6.5)(18.5 - 6.5)}{18.5 + 6.5} = \frac{25 \cdot 12}{25} \]

6. **Cancel out \(18.5 + 6.5\)**:
- The \(25\) in the numerator and denominator cancels out:
\[ = 12 \]

### Final Answer:
The value of the expression is \(12\).

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