Dividing by Zero

a = b
a = ab
a - b = ab-b
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1

The quote is right, you're wrong.

Nice to know someone can't use basic solving GO AMERICA

Damn, I'm having a bad day

Here is where you fail.
a - b = ab-b
(a+b)(a-b) = b(a-b)
It would actually be on the right hand side of the equation either:
= ab-b^2
OR
= b(a-1)

Simple algebra IS pretty tricky. I can see how you would get confused...