What is wrong with the given proof?

Question

Here is the proof they gave: Start with the statement $a = b$. Multiply both sides by $b$ to get $ab = b²$. Subtract $a²$ from both sides to get $ab − a² = b² − a²$. Factor the left and right sides of the equation to get $a(b − a)=(b − a)(b + a)$. Now divide both sides by $b − a$ to get $a = b + a$. Finally, let $a = b = 1$ in this final result to get the statement that $1 = 2$ but that is not true. What went wrong with the proof?

I'm not sure but is the error that you are not allowed to divide by $b-a$?

Division is only an operation can be done if being divided by non zero number — Kamster, Feb 17 '16 at 02:40
You are right. Since a=b, b-a=0 and you are not allowed to divide by zero. (I am, but I am special.) — marty cohen, Feb 17 '16 at 02:42
duplicate: http://math.stackexchange.com/q/1493827/11206 http://math.stackexchange.com/q/117998/11206 — miracle173, Feb 17 '16 at 02:59

score 3 · Accepted Answer · answered Feb 17 '16 at 02:45

3

Dividing by $b-a$ is not allowed. The first line assumes that $a=b$, so $b-a=0$.

answered Feb 17 '16 at 02:45

Stella Biderman

31,475

What is wrong with the given proof?

1 Answers1