Almost 5 years later, I think my answer can reduce a little bit the hard work of many people.
Update an element in the DOM with the HTML from the one from the ajax call can be achieved that way
$('#submitform').click(function() {
$.ajax({
url: "getinfo.asp",
data: {
txtsearch: $('#appendedInputButton').val()
},
type: "GET",
dataType : "html",
success: function (data){
$('#showresults').html($('#showresults',data).html());
// similar to $(data).find('#showresults')
},
});
or with replaceWith()
// codes
success: function (data){
$('#showresults').replaceWith($('#showresults',data));
},