Question

已知x+(y分之1) =z+(x分之1)=1,求y+(z分之1)的值

Answer 1

∵x+1/y = z+1/x = 1

根据x+1/y = 1得：1/y=1-x,y = 1/(1-x)

根据 z+1/x = 1得：z=1-1/x=(x-1)/x,1/z = x/(x-1)

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