20082008分之20092009减20092009分之20102010

20092009 / 20082008 = 1 又 10001 / 20082008 =1 又 1 / 2008
20102010 / 20092009 = 1 又 10001 / 20092009 = 1 又 1 / 2009
∴ 20082008分之20092009减20092009分之20102010
= 1 又 1 / 2008 - 1 又 1 / 2009
= 1 / 2008 - 1 / 2009
= 2009 / 2008 × 2009 - 2008 / 2008 × 2009
= （2009 - 2008）/ 2008 × 2009
= 1 / 2008 × 2009

20092009/20082008-20102010/20092009
=(1+10001/20082008)-(1+10001/20092009)
=1/2008-1/2009=1/(2008*2009)

原式=（2009×10001）/（2008×10001）-（2010×10001）/（2009×10001）=2009/2008-2010/2009=1/4034072