Question

计算（2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)急急急！

计算（2+1/2003+1/2004+1/2005)*(1/2003+1/2004+1/2005+1/2006)-(2+1/2003+1/2004+1/2005+1/2006)*(1/2003+1/2004+1/2005）
急急急！

Answer 1

设1/2003+1/2004+1/2005=a，1/2003+1/2004+1/2005+1/2006=b，则
原式=（2+a)b-(2+b)a
=2b+ab-2a-ab
=2(b-a)
=2(1/2003+1/2004+1/2005+1/2006-1/2003-1/2004-1/2005)
=1/1003

Answer 2

换元法:
设: 1/2003+1/2004+1/2005=a, 1/2003+1/2004+1/2005+1/2006=b,
原式=(2+a)*b-(2+b)*a=2b+ab-2a-ab
=2(b-a)=2/2006=1/1003