what is wrong in this equation?

Question

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

Answer 1

if a=b, then a-b=0
division by zero is not defined
but you proceeded as if it was

Answer 2

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

Taking as a truth that a=b, we can say that the second line is right
The third line, taken that a-b = 0, if you multiply 0 by a, b, or a+b, or anything else, you will always get 0.
The third one, a+b = b, if you solve for it, a would have to be 0 and so would b.

Answer 3

The last parth is the only wrong part the rest is all correct.
a=b so a=a or b=b
a^2=ab so a^2=aa or a^2=bb or a^2=ab
a^2-b^2=ab-b^2 so they are both =0
(a+b)(a-b)=b-(a-b) so that is the difference of squares on the same numbers BUT
a+b=b is not true

Answer 4

This one is so old that I think it was written on the Tree of Knowledge in the Garden of Eden !!!
IF a=b, then a-b= 0 and the 5th step ( not shown above) involves division by a-b and, of course, division by zero has no meaning.

Answer 5

here u have assumed a =b

this implies a-b = 0

you cannot cancel a term that is equal to zero
here you have canceled a-b - that is the mistake


when there is a possibility of a term being equal to zero
u cant cancel it - instead u bring that whole term other side & equate to zero