quick question here:
In my proofs class we had a problem that after a little work we end up with: $x(x-y)=(x+y)(x-y)$ where $ x = y $. Now, I know this is pretty basic, but my teacher said that for the next step, one cannot cancel out $(x-y)$ from both sides as $(x-y) = 0 $. Can someone explain the logic and/or the reasoning behind this?
I'm pretty sure this falls under some obscure basic algebra rule that I've forgotten over the years but I cannot find anything about this on the internet.
To clear up some confusion here, I am not looking for how to solve this problem, but rather the why this particular rule is so.
The problem I am working on gives a proof. I am supposed to mark the errors in the proof. For this problem, the error was that they cancelled out $(x-y)$ and I am trying to understand why that's an error.