Aren't you missing a chomp? Assuming so, sSomething like:

my $fh = open_file( 'filename' );
print read_first_line( $fh );
print read_two_lines( $fh ) until eof( $fh );

sub read_first_line
{
    my $fh = shift;
    return scalar <$fh>;
}

sub read_two_lines
{
    my $fh = shift;
    chomp(my $first = <$fh>);
    return $first . <$fh>;
}
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