Question

化简：根号（a/b+b/a+2）-根号下b/a-根号下a/b+根ab （a＞0，b＞0）

Answer 1

根号（a/b+b/a+2）-根号下b/a-根号下a/b+根ab
= 根号(a^2+b^2+2ab/ab)-根号下b/a-根号下a/b+根ab
=(a+b)*根号(ab)/ab-根号下(ab)/a-根号下(ab)/b+根ab
=根号(ab)[(a+b)/ab-1/a-1/b+1]
=根号(ab)

Answer 2

原式=√[√(a/b)+√(b/a)]²-1/a√ab-1/b√ab+√ab
=1/b√ab+1/a√ab-1/a√ab-1/b√ab+√ab
=√ab.