Question

What's wrong with this proof:

Suppose a = b.
Then:
a^2 = ab | Multiply by a
(a^2) - (b^2) = ab - (b^2) | Subtract (b^2)
(a+b)(a-b) = (a-b)b | Factor
a+b = b | Divide by (a-b)
b + b = b | Substitute a = b
2b = b | Addition
2 = 1 | Divide by b

Answer 1

both of the division steps. you can't divide by (a-b) since a - b is 0 according to the original statement a = b

you also cannot divide by b unless you stipulate that b =/= 0