I was talking about this step:
A(A+B-X)=-B(A+B-X)
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(A+B-X)
Which I assume translates to A(A + B − X) ÷ (A + B − X) = −B(A + B − X) ÷ (A + B − X). A = −B is a valid result from this step in all cases but one: when A + B − X = 0, because division by zero is undefined. Since the second line (A + B = X) specifically states that it
is zero, the proof is invalid.
You can see a similar error in
this proof.