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(a^(2)-b^(2))/(a-b) =...

`(a^(2)-b^(2))/(a-b)` = _______

A

`a+b`

B

`a-b`

C

`a^(2) + b^(2)`

D

`(a-b)^(2)`

Text Solution

AI Generated Solution

The correct Answer is:
To simplify the expression \((a^{2}-b^{2})/(a-b)\), we can follow these steps: ### Step 1: Recognize the Difference of Squares The expression \(a^{2} - b^{2}\) is a difference of squares. We can use the identity: \[ x^{2} - y^{2} = (x - y)(x + y) \] In our case, let \(x = a\) and \(y = b\). Therefore, we can rewrite \(a^{2} - b^{2}\) as: \[ a^{2} - b^{2} = (a - b)(a + b) \] ### Step 2: Substitute Back into the Expression Now, we substitute this back into our original expression: \[ \frac{a^{2} - b^{2}}{a - b} = \frac{(a - b)(a + b)}{a - b} \] ### Step 3: Cancel the Common Factors Since \(a - b\) appears in both the numerator and the denominator, we can cancel these common factors (as long as \(a \neq b\)): \[ \frac{(a - b)(a + b)}{a - b} = a + b \] ### Final Result Thus, the simplified form of the expression \((a^{2}-b^{2})/(a-b)\) is: \[ a + b \] ---
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