[a²/a²-b²-a²b/a²-b²*(a/ab+b²-b/a²+ab)]
={a²(/a²-b²)-a²b/(a²-b²)*(a²-b²)/[ab(a+b)]}
={a²/(a²-b²)-a/[(a+b)]}
=[a²-a(a-b)]/[(a+b)(a-b)]
=b/[a+b)(a-b)]