Mathematical Proof That 2 = 1 Searching for a math impossibility

Try this one
out - see if you can find the hole here!
(Don’t scroll down until you’ve given it a good shot ...)

Initial supposition x = y
Multiply both sides by x: xx = xy
Subtract y squared from both sides: xx - yy = xy - yy
Factor both sides: (x + y)(x - y) = y(x - y)
Divide both sides by (x - y): x + y = y
Substitute y for x, based on initial supposition: y + y = y
Replace y with any number (eg. 1): 1 + 1 = 1 or 2 = 1

Scroll down to see the ‘flaw’ ...

The step that divides through by (x - y) is effectively dividing by zero, based on the
initial supposition. That invalidates the subsequent results.