How to divide the fraction 1 <mrow class="MJX-TeXAtom-ORD"> / </mrow> 1 + 1

Logan Wyatt 2022-07-10 Answered
How to divide the fraction 1 / 1 + 1
This has to do with re-calculating the sigmoid function in ai. It isn't really important, but the simplest way to put it is I need a math guru to help my monkey brain do this:
1 1 + e
to like
1 s o m e t h i n g + 1 e
Please help me remember my math from high-school if this was ever taught to us.
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Answers (2)

Allison Pena
Answered 2022-07-11 Author has 14 answers
The problem is that there isn't really a good way to do that. Things that do work with fractions are the following:
1. a + b c = a c + b c
2. a b c d = a c b d
but there isn't a way to separate when there is a sum in the denominator.
I suppose perhaps one thing you could do, although this isn't likely what you have in mind, is the following: if e is small in your description (that is, if | e | < 1) then there is a geometric series expansion
1 1 + e = 1 e + e 2 e 3 + e 4 + = n = 0 ( 1 ) n e n
but I'm not so certain this is what you're looking for.

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Patatiniuh
Answered 2022-07-12 Author has 5 answers
I suppose that the question is less elementary than only finding 1 1 + e = 1 e 1 e ( 1 + e )
May be you want to express 1 1 + e in terms of 1 e ?
If so, use a geometric series :
1 1 + e = 1 e 1 + 1 e = 1 e ( 1 e ) 2 + ( 1 e ) 3 ( 1 e ) 4 + . . .
1 1 + e = n = 1 ( 1 e ) n

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