Ok i just started learning ajax and i was wondering if i can have the ajax and the php on the same page?

Here's my pages:
register.html
registercheck.php

register.html
Code:
<html>
<head>
<title>Register</title>
<script language="javascript" type="text/javascript">
<!-- 
//Browser Support Code
function checkusername(){
	var ajaxRequest;  // The variable that makes Ajax possible!
	
	try{
		// Opera 8.0+, Firefox, Safari
		ajaxRequest = new XMLHttpRequest();
	} catch (e){
		// Internet Explorer Browsers
		try{
			ajaxRequest = new ActiveXObject("Msxml2.XMLHTTP");
		} catch (e) {
			try{
				ajaxRequest = new ActiveXObject("Microsoft.XMLHTTP");
			} catch (e){
				// Something went wrong
				alert("Your browser do not support ajax!");
				return false;
			}
		}
	}
	// Create a function that will receive data sent from the server
	ajaxRequest.onreadystatechange = function(){
		if(ajaxRequest.readyState == 4){
			var ajaxDisplay = document.getElementById('username_div');
			ajaxDisplay.innerHTML = ajaxRequest.responseText;
		}
	}
	var username = document.getElementById('username').value;
	var query = "?username=" + username;
	ajaxRequest.open("GET", "registercheck.php" + query, true);
	ajaxRequest.send(null); 
}
//-->
</script>
</head>
<body>
<form>
<table border="1" bordercolor="#000000" cellspacing="0">
  <tr>
    <td>Username:</td>
    <td><input type="text" id="username" onkeyup="checkusername()" /></td>
    <td><div id="username_div">Username Status!</div></td>
  </tr>
</table>
</form>
</body>
</html>
registercheck.php
PHP Code:
<?php
$dbhost 
"localhost";
$dbuser "root";
$dbpass "";
$dbname "race";
    
//Connect to MySQL Server
mysql_connect($dbhost$dbuser$dbpass);
    
//Select Database
mysql_select_db($dbname) or die(mysql_error());
    
//Set variables
$username $_GET['username'];
    
//Mysql Variables
$result_query mysql_query("SELECT * FROM `users` WHERE `username`='$username'") or die(mysql_error());
$result_num_rows mysql_num_rows($result_query);

  if(isset(
$username)):
  
    if(
$result_num_rows == 0):
    
    echo 
'<font color="green"><strong>Username avaliable!</strong></font>';
    
    elseif(
$result_num_rows != 0):
    
    echo 
'<font color="red"><strong>Username unavaliable!</strong></font>';
    
    endif;
    
  endif;
?>
I hope someone could help! Thanks anyways!