先化简,再求值:x＋根号xy／根号xy＋y＋根号xy－y／x－xy,其中x＝根号3＋1,y＝根号3－1

题目

先化简,再求值:x＋根号xy／根号xy＋y＋根号xy－y／x－xy,其中x＝根号3＋1,y＝根号3－1

答案

[x＋√(xy)]／[√(xy)＋y]＋[√(xy)－y]/[x－√(xy)]
=[x＋√(xy)]*[√(xy)-y]/(xy-y²)＋[√(xy)－y]*[x+√(xy)]/(x²-xy)
=[x√(xy)-y√(xy)]/[y(x-y)]+[x√(xy)-y√(xy)]/[x(x-y)]
=√(xy)/y+√(xy)/x
=√(xy)(x+y)/xy
=√[(√3+1)(√3-1)](√3+1+√3-1)/[(√3+1)(√3-1)]
=√2*2√3/2=√6
对吗.