does anybody know what happens mathematically when you layer a sound wave over another one?

I was thinking about this last night when I was trying to cut up some loops that I downloaded.

Heres an example:
-I have a kick that I want to extract out of this loop but it has a hi hat on it that I want gone.
-If, when layered, audio files are multiplied together? then would you be able to remove the hi-hat by layering an inverted wav of the hi-hat over the top?
ie. y(x*(1/x)) = y

havent had the time to try it but would it work? If not is there any way to change this so that it could work?

Trying to take out other sounds by EQing just doesnt do it for me because I lose too much of the sound I want.

Jiddu