当x+(x+1)^-1=y+(y-1)^(-1)-2且x-y+2=0，试求xy-x+y

当x+(x+1)^（-1）=y+(y-1)^(-1)-2且x-y+2=0，试求xy-x+y
解：
x+[1/(x+1)]=y+[1/(y-1)]-2
x(x+1)(y-1)+(y-1)=y(x+1)(y-1)+(x+1)-2
x(xy-x+y)+(y-1)=y(xy-x+y)+(x+1)-2
设：xy-x+y=a
ax+(y-1)=ay+(x+1)-2
ax+y-1=ay+x-1
将y=x+2代入
ax+x+1=a(x+2)+x-1
ax+1=a(x+2)-1
2a=o
∴xy-x+y=0