Dogs and cats living together

I'm watching an animated interview of Buckminster Fuller [1] when I see this sequence of equations:

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

And I'm thinking, that looks right, as far as I can remember algebra, but two can't be equal to one, can it?

I had to work through it by hand to find the problem, and now, gentle reader, you get to work through it yourself.

You're welcome.

[1] http://www.openculture.com/2015/03/an-animated-buckminster-fuller-tells-studs-terkel-about-the-geodesic-life.html

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