N/0=Fail

I've seen this posted in various iterations over the last week or so; this latest one is from Darius Whiteplume's Tumblr. See that last step, where they divide both sides by (a-b)? a=b, so a-b=0. In fact, each step from the fourth on is saying 0=0, which is true, but you still aren't allowed to divide it out. These sort of things are fun as long as you don't take them seriously, or if you take them seriously enough to find the sneaky "divide by zero" step. Is that a syncline or a distortion in the space-time continuum? Hard to say when you've divided by zero.