题目

先化简再求值:x/y(x+y) -y/x(x+y)其中x=（根号2）+1,y=（根号2）-1

提问时间：2021-03-24

答案

原式=x²/[xy(x+y)]-y²/[xy(x+y)]
=(x²-y²)/[xy(x+y)]
=(x+y)/(x-y)/[xy(x+y)]
=(x-y)/(xy)
=[(√2+1)-(√2-1)]/[(√2+1)(√2-1)]
=(√2+1-√2+1)/(√2²-1²)
=2/(2-1)
=2