Question

化简根号b分之a+根号a分之b-根号b分之a+a分之b+2(a>0,b>0)

Answer 1

原式=√(a/b)+√(b/a)-√[(a/b)+(b/a)+2] (a﹥0,b﹥0)

=√(ab/b²)+√(ab/a²)-√[(a²+b²+2ab)/(ab)]

=√(ab)/b+√(ab)/a-√[(a+b)²/(ab)]

=[a√(ab)+b√(ab)]/(ab)-(a+b)√[ab/(ab)²]

=(a+b)√(ab)/(ab)-(a+b)√(ab)/(ab)

=0