Nice Try. But I noticed a slight Mathematical Problem (assumeing you are in the set of Real Numbers
=> (a+b)(a-b)=(a-b)
You Dived by a-b to get
=> (a+b)=1
However, if a-b=0 then you divided by zero . . . but one of the postulates in the set of reals states that you cannot divide by 0 because it approaches infinity, which is not in the set of real numbers.
THEREFORE: your proof is inconclusive.
BK
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