(1843/1844)*1845

(1843/1844)×1845=(1843/1844)×1844+(1843/1844)=1843(1843/1844)

2003×(2003/2004)=2004×(2003/2004)-(2003/2004)=2002(1-2004)

设1844=a
原式=(a-1/a)*(a+1)
=(a-1)*(a+1)/a
=(a^2-1)/a
=a - 1/a
=1844 - 1/1844
=1843又1843/1844

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(1843/1844)*1845
=(1844-1)(1844+1)/1844
=(1844^2-1)/1844
=1844-1/1844
=1843又1843/1844

2003*(2003/2004)
=(2004-1)^2/2004
=(2004^2-2*2004-1)/2004
=2004-2-1/2004
=2002-1/2004
=2001又2003/2004

(1843/1844)*1845=(1843/1844)*(1844+1)=(1843/1844)*1844+(1843/1844)*1=1843+(1846/1844)