Question

化简[√ab-ab/(a+√ab)]÷(√ab-a)/(a-b)

Answer 1

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

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

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

= -[√ab - √a*b/(√a+√b)] /√a * (√a+√b)

= -[√b - b/(√a+√b)] * (√a+√b)

= -[√b(√a+√b) - b]

= -[√ab + b - b]

= -√a