作业帮计算:1/a+1-1/a+2+1/a+3-1/a+4计算:1/a+1-1/a+2+1/a+3-1/a+4=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/16 17:09:38
计算:1/a+1-1/a+2+1/a+3-1/a+4计算:1/a+1-1/a+2+1/a+3-1/a+4=?
计算:1/a+1-1/a+2+1/a+3-1/a+4
计算:1/a+1-1/a+2+1/a+3-1/a+4=?
计算:1/a+1-1/a+2+1/a+3-1/a+4计算:1/a+1-1/a+2+1/a+3-1/a+4=?
1/(a+1)-1/(a+2)+1/(a+3)-1/(a+4)
=1/(a+1)-1/(a+4)-[1/(a+2)-1/(a+3)]
=(a+4-a-1)/[(a+1)(a+4)]-(a+3-a-2)/[(a+2)(a+3)]
=3/[(a+1)(a+4)]-1/[(a+2)(a+3)]
=[3(a²+5a+6)-(a²+5a+4)]/[(a+1)(a+4)(a+2)(a+3)]
=(2a²+10a+14)/[(a+1)(a+4)(a+2)(a+3)]
=2(a²+5a+7)/[(a+1)(a+4)(a+2)(a+3)]
1/a抵消，结果为1+2+3+4=10
1/a+1-1/a+2+1/a+3-1/a+4
=1/(a+1)-1/(a+2)+1/(a+3)-1/(a+4)
=1/(a+1)(a+2)+1/(a+3)(a+4)
=[(a+3)(a+4)+(a+1)(a+2)]/(a+1)(a+2)(a+3)(a+4)
=(2a平方+10a+14)/(a+1)(a+2)(a+3)(a+4)
1/a+1-1/a+2+1/a+3-1/a+4
＝[1/﹙a＋1﹚－1/﹙a＋4﹚]－[1/﹙a＋2﹚－1/﹙a＋3﹚]
＝3/﹙a²＋5a＋4﹚－3/﹙a²＋5a＋5﹚
＝3/﹙a²＋5a＋4﹚﹙a²＋5a＋5﹚.
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