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A=Aa+e

A-Aa=e

A(1-a)=e

A=e/(1-a) not e/(e-a)



Nope, I'm pretty sure it's not wrong. I believe ϵ is the multiplicative identity ("1") here. Note that ϵ is the empty string, and concatenating it with anything results in the same thing, so Aϵ = A. Hence we have Aϵ - Aa = A(ϵ - a) = ϵ.




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