SOLUTION: if x= 1-y/1+y and y=1+z/1-z, show that x+z=0

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Question 1190753: if x= 1-y/1+y and y=1+z/1-z, show that x+z=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
x=+%281-y%29%2F%281%2By%29
+y=%281%2Bz%29%2F%281-z%29..........solve for z
y%281-z%29=%281%2Bz%29
y-zy=1%2Bz
y-1=zy%2Bz
y-1=z%28y%2B1%29
z=%28y-1%29%2F%28y%2B1%29

then
x%2Bz=%281-y%29%2F%281%2By%29%2B%28y-1%29%2F%28y%2B1%29
x%2Bz=%281-y%2By-1%29%2F%28y%2B1%29
x%2Bz=0%2F%28y%2B1%29.........quotient of zero divided by any number will be zero
x%2Bz=0