I have this piece of html:
Text for div 2
If you don't need any special functionality given by the full $.ajax method, you should give $.load() a try:
The .load() method, unlike $.get(), allows us to specify a portion of the remote document to be inserted. This is achieved with a special syntax for the url parameter. If one or more space characters are included in the string, the portion of the string following the first space is assumed to be a jQuery selector that determines the content to be loaded.
$('#result').load('ajax/test.html #container');
http://api.jquery.com/load/#loading-page-fragments