Question

Let R be a ring, A a subring of R and B an ideal of R. Then A + B = {a + b | a ∈ A and b ∈ B} is a subring of R (you do not have to prove this) and A∩B is an ideal of A (you do not have to prove this). Prove that A/(A∩B) ∼= (A+B)/B