To simplify the given expression, we can first factor the numerator and denominator of the left side:
(A^3 - B^3) / (A^2 + AB + B^2) = ((A - B)(A^2 + AB + B^2)) / (A^2 + AB + B^2) = A - B
Therefore, the given expression simplifies to:
(A^3 - B^3) / (A^2 + AB + B^2) = (A - B) / (A - B) = 1
So, the simplified expression is 1.
To simplify the given expression, we can first factor the numerator and denominator of the left side:
(A^3 - B^3) / (A^2 + AB + B^2) = ((A - B)(A^2 + AB + B^2)) / (A^2 + AB + B^2) = A - B
Therefore, the given expression simplifies to:
(A^3 - B^3) / (A^2 + AB + B^2) = (A - B) / (A - B) = 1
So, the simplified expression is 1.