division by zero

Long ago, a clever mathematician used to cheat people.
Once he borrowed Rs.4000/- from a rich man. After a
few days, he borrowed Rs.2000/- from the same man.
Many days passed, the mathematician did not return the
money to the rich man. The rich man went to the
mathematician and asked to return the money. But to
his great surprise, the mathematician replied that
there is no need to pay the debt.

"See here, friend" said the mathematician " the sum of
4000 and 2000 is equal to zero, so I do not have any
balance to pay".

The rich man took the matter to the court. When the
judge came to know this, he was astonished. He asked
the mathematician to prove that sum of 4000 and 2000
is zero, and not 6000.

The Clever mathematician agreed. He said:

let a = 4000, b = 2000 and c = 6000

a + b = c

Multiply both sides by a + b

(a + b) (a + b) = c (a + b)

a*a + ab + ba + b*b = ca + cb

a*a + ab - ca = cb - b*b - ba

a( a + b -c) = -b(b + a - c)

so a = - b

a + b = 0
ANSWER IS---!- in this problem have a(a+b-c)=-b(b+a-c). now we divided both the side with a+b-c.
which is eqal to zero.in maths division by zero is a not defined
concept.so it is wrong step.