I'm afraid you violated some algebra rules after the first step.

y = xz + z - x 

Isolate all the terms that contain z on one side of the equation
(You did that correctly, but after that it was all incorrect):

y + x = xz + z

Factor out z on the side you isolated z terms on, which is the right
side in this case:

y + x = z(x + 1)

Divide both sides by (x + 1)

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

Cancel the (x + 1)'s on the right

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

y + x      
-----  =  z
x + 1     

That's the final answer.  Don't try to go any further.


Edwin