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I thought the prob is in the 4th step. I've put my solution as comment in the post :
4th step. a-b is 0 and 0*(any number) is 0. We are actually taking common factors out of the equation 0 = 0. Does 2 * 0 = 5 * 0 , necessarily mean 2 = 5 ? It’s all the 0′s play :)