Question

What is wrong with the following proof?

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

Answer 1

Even if you cancel the a out, there is no actual variable to solve for. This the only solvable solution to this problem would be 0 in rational terms. 1=2 does not signify conclusive result for a variable, its just a clever way to use basic applications of algebra to prove a point which is not in direct relation to the answer.

Answer 2

Since you assume a=b, then dividing by (b-a) would mean dividing by 0.

Answer 3

Precisely^