Four equals to three

Algebra Level 2

Kimmie wants to prove that 4=34=3.

She starts off with the equation ab=ca-b=c which is equivalent to

4a3a4b+3b=4c3c \large 4a-3a-4b+3b = 4c-3c

She moved the variables to obtain 4a4b4c=3a3b3c4a-4b-4c = 3a-3b-3c and factorized it to

4(abc)=3(abc)\large 4(a-b-c) = 3(a-b-c)

Finally, she cancelled both sides to obtain 4=3 4=3.

What is the error in Kimmie's work?

Image credit: IIT Bombay.

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