(a / (√(ab) - b) - √b / (√b - √a)) * (√a - √b) * b / (a + b) =
(a / (√b(√a - √b) + √b / (√a - √b)) * (√a - √b) * b / (a + b) =
(a / (√b(√a - √b) + b / (√b (√a - √b)) ) * (√a - √b) * b / (a + b) =
(a + b) / (√b(√a - √b)) * (√a - √b) * b / (a + b) =
(a + b) / √b * b / (a + b) =
√b