The person before made a mistake in their proof.
1. x = y
2. xy = y^2
3. xy - x^2 = y^2 - x^2
4. x(y - x) = (y + x)(y - x)
So far so good.
4.5. x = (y + x)(y - x)/(y - x) is what they did to get to step 5, which says:
5. x = y + x

This is wrong though. since x = y, y -x = 0, and so you can't divide by y - x.

1. x = y
2. xy = y^2
3. xy - x^2 = y^2 - x^2
4. x(y - x) = (y + x)(y - x)
5. x = y + x
6. x = x + x
7. x = 2x
8. 1 = 2

QED