If `(a^(2) - b^(2)) div (a + b) = 25`, find `a-b`.
A. 15
B. 18
C. 25
D. 30

Options

A. C
B. D
C. A
D. B

Answer

To solve the equation \( \frac{a^2 - b^2}{a + b} = 25 \) and find the value of \( a - b \), we can follow these steps:

### Step 1: Use the difference of squares identity
We know from algebra that \( a^2 - b^2 \) can be factored as:
\[ a^2 - b^2 = (a + b)(a - b) \]
So we can rewrite the equation as:
\[ \frac{(a + b)(a - b)}{a + b} = 25 \]

### Step 2: Simplify the equation
Since \( a + b \) is in both the numerator and the denominator, we can cancel it out (assuming \( a + b \neq 0 \)):
\[ a - b = 25 \]

### Step 3: Identify the value of \( a - b \)
From the simplified equation, we find that:
\[ a - b = 25 \]

### Conclusion
Thus, the value of \( a - b \) is \( 25 \).