不希望.htaccess更改我的网址链接

I am currently creating multiple subdomain handeling system. I don'know how to set the .htaccess until I found this tutorial at Youtube.

I followed the original source code:

    RewriteEngine on
    RewriteCond %{HTTP_HOST} !^www.your_domain.com
    RewriteCond %{HTTP_HOST} ^([^.]+).your_domain.com
    RewriteRule ^$ /index.php?name=%1 [L] 

And I modify it to:

    RewriteEngine on

    RewriteCond %{HTTP_HOST} !^www.mlaxproject.com
    RewriteCond %{HTTP_HOST} ^([^.]+).mlaxproject.com
    RewriteRule ^$ /sub_website/%1

It is almost completed; the URL takes me to the correct directory, but the only problem is that it reveals the sub directory at my URL:

expect result : demos.mlaxproject.com
show result :demos.mlaxproject.com/sub_website/demos/

How I would like it to be:

demos.mlaxproject.com
test.mlaxproject.com
hello.mlaxproject.com

And not:

demos.mlaxproject.com/sub_website/demos/
test.mlaxproject.com/sub_website/test/
hello.mlaxproject.com/sub_website/hello/

which is what I am getting,

Thanks and sorry for my English.