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)_数学解答

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)

人气：490 ℃　时间：2020-05-31 09:15:04

解答

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