提公因式竞赛题公因式(2010³-2010²-2009)÷(2010³+2010²
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/10/10 17:22:45
提公因式竞赛题
公因式(2010³-2010²-2009)÷(2010³+2010²-2011)
公因式(2010³-2010²-2009)÷(2010³+2010²-2011)
分子
2010³-2010²-2009
= 2010³-2010²-2010 + 1
= 2010(2010²-1) -(2010²-1)
= (2010 - 1)(2010²-1)
= 2009(2010²-1)
分母
2010³+2010²-2011
= 2010³+2010²-2010 - 1
= 2010(2010²-1) +(2010²-1)
= (2010 + 1)(2010²-1)
= 2011(2010²-1)
所以 (2010³-2010²-2009)÷(2010³+2010²-2011)
= 2009(2010²-1)/2011(2010²-1)
= 2009/2011
2010³-2010²-2009
= 2010³-2010²-2010 + 1
= 2010(2010²-1) -(2010²-1)
= (2010 - 1)(2010²-1)
= 2009(2010²-1)
分母
2010³+2010²-2011
= 2010³+2010²-2010 - 1
= 2010(2010²-1) +(2010²-1)
= (2010 + 1)(2010²-1)
= 2011(2010²-1)
所以 (2010³-2010²-2009)÷(2010³+2010²-2011)
= 2009(2010²-1)/2011(2010²-1)
= 2009/2011
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