Question

请将下列二次根式化简：

Answer 1

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

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

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

=[ a√(ab)/(a+√ab) ]×[ (√a+√b)/√b ]

={ a√a/[√a(√a+√b) ] }×(√a+√b)

=a