I have a JavaScript variable which holds an HTML page and due to the setup I need to extract everything between
This will not be possible with just a regular expression unless the HTML inside that div contains no other divs. Because what will happen with a pattern like Jeremy's is that it will match the first closing div tag, which wouldn't necessarily be the closing tag for the div#LiveArea element.
If you have control over the source HTML, you could insert a comment that you could use to match on for the correct "closing" location.
There are other javascript-only options, but they are each very kludgy or hacky