I'm only an arts student, but I still did a bit of math in my day. Using the fantastic equipment available to me I can't seem to get around not enjoying this. Hit me if this old news, I just get bored and start doing random.

a = b

a2 = ab

a2 - b2 = ab - b2

(a+b)(a-b) = b(a-b)

a+b = b

a+a = a

2a = a

2 = 1

And with that, everything makes sense now!

Main point asking, how does this make sense? I know in arts 'beer = dinner' but in the realm of math, can such atrocities exist?