Here's a another solution. It takes two array refs, makes copies of them, and cancels out common terms, removing all 1's.

sub list_reduce {
  my ( $top, $bot ) = map [ grep $_ != 1, @$_ ], @_;
  die "Bad data\n" if ( grep $_ < 1, @$top, @$bot );
  OUTER:
  for my $i ( reverse 0 .. $#$top ) {
    for my $j ( reverse 0 .. $#$bot ) {
      ( $top->[ $i ], $bot->[ $j ] ) = reduce( $top->[ $i ], $bot->[ $
+j ] );
      splice @$bot, $j, 1 if $bot->[ $j ] == 1;
      if ( $top->[ $i ] == 1 ) {
        splice @$top, $i, 1;
        next OUTER;
      }
    }
  }
  return ( $top, $bot );
}

sub reduce {
  my ( $top, $bottom ) = @_;
  my $gcd = Math::BigInt::bgcd( $top, $bottom );
  return ( $top/$gcd, $bottom/$gcd );
}
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