I was expecting this mess.
And I was expecting it to replicate the behavior of the John Knoll Unmult After Effects plugin.
Oh well, I hear The Gimp does it.
It turns out that in the mathematical expression you want the RGB in the numerator and the ALPHA in the denominator, but in Photoshop you want the alpha image in the upper layer.
Success. I think. :)
So if you layer mask that hot mess above by the original grayscale alpha key at the top of this thread then all the ugly parts go away and you should be left with a beautiful comp.
-- using a layer mask. (which you could 'apply' if you wish)
The side on the right has the ugly RGB element which makes the nice comp results.
(more conversation here)
There is an old use of the divide blend mode from 1983 that I know of in the Disney / John Lasseter cg test for a film based on Maurice Sendak's Where the Wild Things Are.
It involved drawing shapes with hard lines, blurring them to look like CG, and dividing the blurred shapes by their own masks so that the interiors had nice soft 'shading' but the blur didn't introduce darkness around the edge of every shape because the edges received equal blur and were given the 'divide' treatment.
The interior of the masks were white. Anything divided by white (1) is unchanged (left blurry)
The edges were normalized back to their original colors by being divided by the soft masks.
The divide blend mode is written to skip pure black pixels, as division by zero is undefined.