2009³-2×2009²-2007/2009³+2009²-2010

2009³-2×2009²-2007/2009³+2009²-2010
2009³-2×2009²-2007/2009³+2009²-2010

2009³-2×2009²-2007/2009³+2009²-2010
2009³-2×2009²-2007/2009³+2009²-2010
=2009²×(2009-2)-2007/2009²×(2009+1)-2010
=2009²×2007-2007/2009²×2010-2010
=2007×(2009²-1)/2010×(2009²-1)
=2007/2010
=669/670

令a=2009
则2007=a-2,2010=a+1
原式=[a³-2a²-(a-2)]/[a³+a²-(a+1)]
=[a²(a-2)-(a-2)]/[a²(a+1)+(a+1)]
=(a²-1)(a-2)/(a²+1)(a+1)
=(a-2)/(a+1)
=2007/2010
=669/670

[2009³-2×2009²-2007]/[2009³+2009²-2010]
=[2009²(2009-2)-2007]/[2009²(2009+1)-2010]
=[2007(2009²-1)]/[2010(2009²-1)]
=2007/2010