Using Select-String against a server list - powershell

Question

I have a serverlist which contains all server names on a single line. Each server has the exact path and file as listed in the following:
$Computers = get-content "c:\temp\serverlist.txt"
foreach ($Computer in $Computers) {
select-string "F:\xxx\SmarXXXX\yyyyyyations\xxxxx\servers\data-sources.xml" `
-pattern "thisiswhatimsearchingfor"
}
I edited the actual code with xxxxx since some of it may be considered sensitive. When I run this command I am given the string that I am looking for, but there is no link to which server returns this data. I essentially need to find out which servers from my serverlist do NOT contain the pattern requested.
Any ideas would be appreciated. Thanks for your patience.
EDIT:
I have come up with the following but it does not display the desired output. This returns just the strings, but not the servers that it is pulling them from. Thanks for the help. I attempted to add the where-object in order to see the associated server with each string. This failed.
$Computers = get-content "c:\temp\serverlist.txt"
foreach ($Computer in $Computers) {
Select-String "F:\xx\xxxxxxPath\applications\yyyyyyy\servers\data-xxxx.xml" -pattern "render" | where {($_ -match "render")
}
}

Answer 1

Use UNC paths and a filter to get a list of computers where the search pattern occurs in the file:
$file = 'F$\xxx\SmarXXXX\yyyyyyations\xxxxx\servers\data-sources.xml'
Get-Content "c:\temp\serverlist.txt" | ? {
(Get-Content "\\$_\$file") -match 'search pattern'
}

Answer 2

This might do it:
Get-Content c:\temp\serverlist.txt | where {
-not ( $_ -match "thisiswhatimsearchingfor" )
}