Thanks for finding a solution guys and gals. Just saved me the headache of having to remove the word "remove" appended on the end of each line in a document with 300 lines.

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I changed it a little bit, posted below:
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#!perl
print "What is the name of the file you want to remove a word ar phras
+e from? \nPlease include the extension. \n";
chomp(my $rem_name = <STDIN>);
print "Please enter a word ar phrase you want to remove: \n";
chomp(my $replacestring = <STDIN>);
open(my $infile,"<","$rem_name") or die $!;
open (my $outfile,">","outputfile.txt") or die $!;
while (<$infile>)
{
    $_=~s/$replacestring//g;
    print $outfile $_;
}
close $infile;
close $outfile;
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