How to Show 1=0 With Algebra... Test Your Understanding

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Ok, so obviously 1 is not equal to 0, but I will go through a simple few lines of algebra that seem reasonable at first glance, but lead to the shocking conclusion that 1=0. It is a good test of your basic understanding to show me why this is wrong... see if you can find the error and let me know!

We start with the equation


Now multiply both sides by x to get

 x^2 = x.

Subtracting one from both sides gives

 x^2 - 1 = x-1.

Factorize the left hand side and divide both sides by x-1.

 \frac{(x+1)(x-1)}{(x-1)} = \frac{(x-1)}{(x-1)}

The (x-1) factors cancel to leave

 x+1 = 1,



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