To simplify the expression, first factorize the denominator by using the difference of squares formula:

(a^2 - b^2) = (a + b)(a - b)

Therefore, the expression becomes:

(a^3 - b^3) / (a^2 - b^2)(a + b)

Next, use the formula for the difference of cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Substitute this back into the expression:

(a - b)(a^2 + ab + b^2) / (a + b)(a - b)(a + b)

Cancel out the common factors:

= (a^2 + ab + b^2) / (a + b)

So, the simplified expression is (a^2 + ab + b^2) / (a + b).