Apache Redirect Transparently

I have two servers running apache server, namely server A and B.

All users access server A, but for some application, I would like to redirect the request to server B.

I have set apache redirect in server A apache config file.
Redirect /application http://serverB/application

Now, the flow becomes

  1. Users input http://serverA/application
  2. Redirect request to http://serverB/application
  3. Users see the web page changed from http://serverA/application to http://serverB/application

Actually, I do not prefer users to see the web page changed. Is there any method that can redirect the request transparently to user?
Thank you!

Helo alfredo.
For that purposes, I usually use mod_proxy and configure Apache as a reverse proxy like this, on your serverA (for Apache 1.3):

ProxyRequests Off

<Directory proxy:*>
   Order Deny,Allow
   #Deny from all
   Allow from all
</Directory>

ProxyPass /application http://serverB/application
ProxyPassReverse /application http://serverB/application

Regards.

Thank you very much!
This is exactly what I want.
Thanks!