You're doing it wrong, and you don't need to use live.

I tested this, and it works:

var $results = $('#ajaxSearchResults');
$('<span></span').text('(close)').appendTo($results).click(function(){
    $(this).parent().hide('slow');
});

First we cache the #ajaxSearchResults into a var. Then we create an
empty span, add some text to it, and then append it to our cached div.
Then we add a click action to it, and tell it that it should hide it's
parent, when clicked.

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