Why are the different input elements separated into different FORM tags? You're only going to get the data from one form.
EDIT: Also, one other error:
if ($operation = "add"){
Here, you're using the assignment operator, thus the value of $operation is set to "add". I suspect you wanted to use a comparison operator instead (e.g. a double equal sign). See this page for more info: [man]operators.comparison[/man].
You should also know that the '<?' (and '<?=') short tags have long ago been deprecated. You should always use the full '<?php' tag in all PHP scripts.