How about this one then?
* Let a and b be equal non-zero quantities
a = b
* Multiply through by a
a^2 = ab
* Subtract b^2
a^2 − b^2 = ab − b^2
* Factor both sides
(a − b)(a + b) = b(a − b)
* Divide out (a − b)
a + b = b
* Observing that a = b
b + b = b
* Combine like terms on the left
2b = b
* Divide by the non-zero b
2 = 1
How about this one then?
* Let a and b be equal non-zero quantities
a = b
* Multiply through by a
a^2 = ab
* Subtract b^2
a^2 − b^2 = ab − b^2
* Factor both sides
(a − b)(a + b) = b(a − b)
* Divide out (a − b)
a + b = b
* Observing that a = b
b + b = b
* Combine like terms on the left
2b = b
* Divide by the non-zero b
2 = 1