Equation that proves 1 = 2. Is it correct

Just a little puzzle. Feel free to share any of your own.
We start with a simple
a = b
Multiply both sides by a
a^2 = ab
Add a^2 to each side
2a^2 = a^2 + ab
Minus 2ab from each side
2a^2 - 2ab = a^2 - ab
Factorise the left hand side
2 (a^2 - ab) = a^2 - ab
Divide by a^2 - ab
2 = 1

Hmm. Have something gone wrong?

No it's not.
Your second step states that a^2 = ab.
So a^2 - ab = 0.
In your last step you divide by this, which is not possible, you can't divide by 0.
So, this equation is not true :)

You end up with 0/0 which is indeterminate. Using limits, 0/0 can be shown to take any value so that is why it is indeterminate. I.e. you can't determine what value it is.

e is the constant which is approx. 2.718 but is irrational.

Consider this limit:

(eⁿ-n-1)/(n²) as n->0.
This approaches 0/0 but using l'hopitals rule it can be shown to approach 0.5. Limits that approach 0/0 can have any number as their limit.

If a=b then a^2=ab follows. But on the line before your conclusion
you divide by a^2-ab which =0, and this is not possible so your result
does not follow.

you divided by 0 in the last step.

*yawns*

Where did the one come from?

ur mistake:

since a^2 = ab. lets hacve a^2=ab=x.

u have us divide by x-x. That would be 0. you cant divide by 0