[√ab-ab/(a+√ab)]÷(√ab-b)/(a-b)
=(a√ab+ab-ab)/(a+√ab)×(a-b)/(√ab-b)
=a√ab/√a(√a+√b)×(√a+√b)(√a-√b)/√b(√a-√b)
=a√b/(√a+√b)×(√a+√b)/√b
=a