[Javascript] DIV visibility

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I have two DIVs on the same page, that overlap each other. One has its style 
set to  visibility: visible; and the other's style is set to visibility: 
hidden; After some javascript completes, I hide the first DIV, and then show 
the second one.

However, I have had a complaint that my method of hiding and then showing is 
not working for one guy. Rather than show you my code, I will instead ask 
the following:

What is the best, absolutely bomb-proof method to change the visibility from 
visible to hidden, and from hidden to visible, for the following:

<div id="result"> blah blah blah </div>

It should work for *nearly everybody* (haha)

Tim in Engalnd