$result = mysql_query("SELECT url, title FROM fappageinfo WHERE title LIKE '%{$searchstring}%' ORDER BY dateadded DESC") or die('error database');

$result = mysql_query("SELECT url, title FROM fappageinfo WHERE title LIKE '%{$searchstring}%' OR title LIKE '{$searchstring}%' ORDER BY dateadded DESC") or die('error database');

<?php
// This could be supplied by a user, for example
$firstname = 'fred';
$lastname  = 'fox';

// Formulate Query
// This is the best way to perform an SQL query
// For more examples, see mysql_real_escape_string()
$query = sprintf("SELECT firstname, lastname, address, age FROM friends 
    WHERE firstname='%s' AND lastname='%s'",
    mysql_real_escape_string($firstname),
    mysql_real_escape_string($lastname));

// Perform Query
$result = mysql_query($query);

// Check result
// This shows the actual query sent to MySQL, and the error. Useful for debugging.
if (!$result) {
    $message  = 'Invalid query: ' . mysql_error() . "\n";
    $message .= 'Whole query: ' . $query;
    die($message);
}

// Use result
// Attempting to print $result won't allow access to information in the resource
// One of the mysql result functions must be used
// See also mysql_result(), mysql_fetch_array(), mysql_fetch_row(), etc.
while ($row = mysql_fetch_assoc($result)) {
    echo $row['firstname'];
    echo $row['lastname'];
    echo $row['address'];
    echo $row['age'];
}

// Free the resources associated with the result set
// This is done automatically at the end of the script
mysql_free_result($result);
?>

while ($row = mysql_fetch_assoc($result)) {
    echo $row['url'];
    echo $row['title'];
}

//SQL Connection
$conn = new mysqli($servername, $username, $password, $dbname);
// Check connection
if ($conn->connect_error) {
    die("Connection failed: " . $conn->connect_error);
} 


$sql = "SELECT url, title FROM fappageinfo WHERE title LIKE '%{$searchstring}%' OR title LIKE '{$searchstring}%' ORDER BY dateadded DESC";
$result = $conn->query($sql);

if ($result->num_rows > 0) {
    // output data of each row
    while($row = $result->fetch_assoc()) {
      echo "<div>";
      echo "<a href=\"http://www.faprush.com/";
      echo $row['url'];
      echo "\"";
      echo " target=\"_blank\"";
      echo ">";
      echo $row['title'];
      echo "</a>";
      echo "</div>"; 
}
}

// Closing connection
$conn->close();

<?php

echo "start of program<br><br>\n";

//error_reporting(0);

echo "In new code<br>\n";

require_once('srchdbfunctions.php');

echo "hooking up<br>\n";

$db=hookup('gfy_test');

if($db)
{
  echo "got db <br>\n";
}

echo "past connect<br>\n";

$searchstring='transvestite threesome tea party';

echo "searchstring=" . $searchstring . "<br>\n";

$terms=explode(' ',$searchstring);

echo "Constructing conditions<br>\n";

$conditions=array();
for($i=0;$i<count($terms);$i++)
{
  if(!empty($terms[$i]))
  {
    $conditions[$i]="title like '%" . trim($terms[$i]) . "%'";
  }
}

echo "Constructing sql str<br>\n";

$sql_str  ="select id, url, title from test_table where ";
for($i=0;$i<count($conditions);$i++)
{
  if($i>0)
  {
    $sql_str .=" or ";
  }
  $sql_str .=$conditions[$i] . " ";
}
echo "sql string=" . $sql_str . "<br>";

$stmnt=$db->query($sql_str);

echo "Sql returned " . $stmnt->rowcount() . " rows<br><br>\n";

while($result=$stmnt->fetch(PDO::FETCH_ASSOC))
{
  echo "Rec " . $result['id'] . " Title: " . $result['title'] . " matched <br>\n";
}

echo "<br><br>";


//version 2
?>

Broke this out of html to show how the sql str is being constructed:

$sql_str  ="Select id, url, title from test_table ";
$sql_str .="where title LIKE '%{$searchstring}%'";
<br><br>
As soons as we show it in php the brackets {} disappear:
<br><br>
<?php

echo "sql starts back here:<br>\n";
$sql_str  ="Select id, url, title from test_table ";
$sql_str .="where title LIKE '%{$searchstring}%'";

echo "sql=" . $sql_str . "<br><br>\n";

echo "when we go to execute that we get back:<br><br>";

$stmnt=$db->query($sql_str);

echo "Sql returned " . $stmnt->rowcount() . " rows<br><br>\n";

while($result=$stmnt->fetch(PDO::FETCH_ASSOC))
{
  echo "Rec " . $result['id'] . " Title: " . $result['title'] . " matched " . $result['title'] . "<br>\n";
}

echo "End of program<br>\n";

?>

$trimstring = trim($outputsearchstring, " \t\n\r\0\x0B");

$sql = "SELECT url, title FROM fappageinfo WHERE title LIKE '%$trimstring%' ORDER BY dateadded DESC";