Redirection to subfolder does not allow ajax request (.htaccess)

I have this folder structure

root/
  app/
  public/
      index.php
  .htaccess

The htacces contains:

<IfModule mod_rewrite.c>
    RewriteEngine on
    RewriteRule ^$ public/ [L]
    RewriteRule (.*) public/$1 [L]
</IfModule> 

But it does not allow me to make ajax requests to the folder app/, it redirects me to index.php, I want the same functionality but I only allow pass my ajax requests.