Ajax :: Refresh Page Once - Show The Change In Content Caused By The Delete

I have a php webpage that has a single input box. When ever an item is entered and the Submit button is pressed, the entry is added to a database. Additionally, the database table contents are read and printed directly below the input box and the submit button on the same page, using AJAX. Now, I have decided to add additional functionality to the page. I want a delete button for each entry displayed in the table below. For any button that is pressed, I want to delete that entry from the database.

Here's the problem: I want the database table contents that has been printed below to reflect this change. I can achieve the delete, but in order to show the change in content caused by the delete, the table below must either be replaced or updated via ajax. How can I achieve this? I have been trying to follow these examples using jQuery and Mootools respectively, but I've been having no luck. [URL] I don't want all the fancy looks, I just want the core functionality.