已知x+y=2,xy=1,求(y+1/x+1)+（x+1/y+1）的值,

已知x+y=2,xy=1,求(y+1/x+1)+（x+1/y+1）的值,
已知x+y=2,xy=1,求(y+1/x+1)+（x+1/y+1）的值,

已知x+y=2,xy=1,求(y+1/x+1)+（x+1/y+1）的值,
x+y=2,xy=1,
解得
x=y=1
所以
(y+1/x+1)+（x+1/y+1）
=（1+1）/(1+1)+（1+1）/(1+1)
=1+1
=2

x+y=2,xy=1
x²+y²=(x+y)²-2xy=4-2=2
所以
(y+1)/(x+1)+(x+1)/(y+1)
=[(y+1)²+(x+1)²]/(x+1)(y+1)
=(x²+y²+2x+2y+2)/(xy+x+y+1)
=[x²+y²+2(x+y)+2]/[xy+(x+y)+1]
=(2+4+2)/(1+2+1)
=8/4
=2

x+y=2,xy=1
x=1,y=1

通分之后在合并，合理转换即可。

原式=[(y+1)²+(x+1)²]/[(x+1)(y+1)]
=(y²+2y+1+x²+2x+1)/(xy+x+y+1)
=(x²+y²+2（x+y）+2)/(1+2+1)
=[(x+y)²-2xy+2(x+y)+2]/4
=(4-2+2*2+2)/4
=2