Putting PHP code inside of PHP code?

Probably not saying it right. I have the Add This plugin that allows you to login with your social network to leave a comment. It gives you a small line of PHP code:

<?php addthis_ssi();?>

to add into the PHP of your theme. I was hoping to put it inside of the last line of code in the editor section “Comments.php” inside of the last line of code:

<?php comment_form(); ?>

as opposed to just above it. It works fine just above it for the posts, but unfortunately the Sign in and social networks are shown on all pages and posts whether comments are enabled or not. I just want it to be shown when the actual comment box is shown. Unfortunately I don’t want to think it’s as easy as doing something like this:

<?php addthis_ssi();? <?php comment_form(); ?>>

because I’m quite sure I’d be headed to my file manager afterwards when my whole site got thrown into oblivion. Thank you for any help in this matter.