2001×(1/8 - 1/2009) + 8×(1/2001 - 1/2009) - 2009×(1/8 + 1/2001) + 8
= 2001/8 - 2001/2009 + 8/2001 - 8/2009 - 2009/8 - 2009/2001 + 8
= (2001/8 - 2009/8) + (-2001/2009 - 8/2009) + (8/2001 - 2009/2001) + 8
= (-8/8) + (-2009/2009) + (-2001/2001) + 8
= (-1) + (-1) + (-1) + 8
= 5