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)
问题描述：
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)
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