To simplify this expression, we can start by factoring the numerator and denominator of the second term in the expression.

Numerator of the second term: a³ - b³ = (a - b)(a² + ab + b²)
Denominator of the second term: (a² - b²)(a + b) = (a - b)(a + b)(a + b)

Plugging in these factorizations, we get:

a³ - b³ / (a² - b²)(a + b)
= (a - b)(a² + ab + b²) / (a - b)(a + b)(a + b)
= (a² + ab + b²) / (a + b)(a + b)
= (a + b)² / (a + b)(a + b)
= (a + b)

Therefore, the simplified expression is:

a + b