已知x+(1/y)=z+(1/x)=1,求y+(1/z)

问题描述:

已知x+(1/y)=z+(1/x)=1,求y+(1/z)

x+1/y=1
1/y=1-x
y=1/(1-x)
z+1/x=1
z=1-1/x
z=(x-1)/x
1/z=x/(x-1)
y+1/z=1/(1-x)+x/(x-1)
=-1/(x-1)+x/(x-1)=1