搜搜做题作业网计算:1/(x+3)(x+4)+1/(x+4)(x+5).1/(x+99)(x+100)
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/06/30 12:23:42
计算:1/(x+3)(x+4)+1/(x+4)(x+5).1/(x+99)(x+100)
1/(x+3)(x+4)+1/(x+4)(x+5).1/(x+99)(x+100)
=1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)+.+1/(x+99)-1/(x+100)
=1/(x+3)-1/(x+100)
=(x+100)/[(x+3)(x+100)]-(x+3)/[(x+3)(x+100)]
=(x+100-x-3)/[(x+3)(x+100)]
=97/[(x+3)(x+100)]
=1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)+.+1/(x+99)-1/(x+100)
=1/(x+3)-1/(x+100)
=(x+100)/[(x+3)(x+100)]-(x+3)/[(x+3)(x+100)]
=(x+100-x-3)/[(x+3)(x+100)]
=97/[(x+3)(x+100)]
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