Hello Sergey,
If you have to use that URL then you haven't installed FuelPHP as per the recommendations, but you have installed everything inside your webservers docroot. The recommendation is to make the public folder your docroot, so everything else is outside it (as it's one level up).
If you can't do that (for example because you don't have the server access), the public folder isn't needed. Just move the .htaccess, index.php and the assets folder one level up (so they are in your docroot), and remove the public folder.
That is a lot easier then trying to get rid of the 'public' folder in the URL through .htaccess.