Let be the basic equation.

Then, both sides multiply with .

.

.

Move from left to right; and and from right to left.

.

Factoring …

Removing …

And we have:

.

Oops. It contradicts with our basic equation.

Obviously something is wrong here.

Guess what is the mistake here? It is a primary school’s question in fact π

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a+b=c. equating both sides to 0, a+b=0, assuming c=0. this is one way. thus a=-b.

it could go on and on… a+b=1, assuming c=1…. thus a=1-b

it could go on and on and on.. in the end. if we want an exact answer to a mathematical equation, we would have to make an ass out of you and me. assumptions. π

Bravo.

You have pointed up the keyword. We should never divide something with zero as “1/0” is undefined in Mathematic.

What you mean is,

If a=-b, then c=0 and hence (a+b-c)=0. So

a(a+b-c)=-b(a+b-c), here we can’t cancel the (a+b-c)?

So it is a contradiction?

and 1+1=2.

Good observation. Got pandai π

Sorry. What I mean is, for any a,b,c \in Real number field, if we state an equation as a+b=c, it implies that a+b+c=0. And, we should not divide zero in the algebra manipulation as 1/0 is undefined in first place.

Besides, it is a mistake for not stating what field a, b and c are in a first place.