# I feel like a dunce. I can't find the error

#### slider142

In line 7, B - C - A = 0. The equation A*0 = B*0 does not imply that A = B.

#### pwsnafu

The use of A, B and C is to obfuscate what is going on. If you substitute in the values, it is obvious.

Line 7:
$$A(B-C-A) = B (B-C-A)$$
He then divided by B-C-A.

But B-C-A = 0, and so Line 7 is nothing more than
$$4 \times 0 = 5 \times 0$$

#### mrspeedybob

I see.
So the lesson learned here is that when deviding both sides of an equation by anything the resulting equation is only valid where that thing ≠0
Thanks.

#### Mark44

Mentor
I see.
So the lesson learned here is that when deviding both sides of an equation by anything the resulting equation is only valid where that thing ≠0
Thanks.
A shorter way of saying that is that you can't divide both sides of an equation by zero.