Scott Dattalo wrote:
>
> On Mon, 13 Nov 2000, M. Adam Davis wrote:
>
> > y = ( 1 + x ) / ( 1 - x )
> >
> > simplifies to
> >
> > y= 2 / (1-x) - 1
> > or
> > y= ( -2 / (x-1) ) - 1
>
> I think you meant:
>
>   y  = 1 + 2x /(1-x)
>
> Right?

Well, no:

y = ( 1 + x ) / ( 1 - x )
Seperate the numerator into two fractions:
y = 1/(1-x) + x/(1-x)
Expand using partial fractions:
y = 1/(1-x) + 1/(1-x) - 1
Simplified:
y = 2/(1-x) - 1

This can be simplifed further, knowing that 0 < x < 1, and shouldn't be
too difficult to calculate more quickly than a full 24-bit division
routine.

-Adam

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