SOLUTION: if x+1/y=1 & y+1/z=1 then prove that z+1/x=1

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Question 857700: if x+1/y=1 & y+1/z=1 then prove that z+1/x=1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%2B1%2Fy=1
2.y%2B1%2Fz=1
From eq. 2,
y=1-1%2Fz
y=%28z-1%29%2Fz
1%2Fy=z%2F%28z-1%29
Substitute into eq. 1,
x%2Bz%2F%28z-1%29=1
%28z-1%29x%2Bz=z-1
zx-x%2Bz=z-1
zx-x=-1
zx=-1%2Bx
z=%28x-1%29%2Fx
z=1-1%2Fx
z%2B1%2Fx=1