作业帮1/(x-1)x+1/x(x+1)+.+1/(x+9)(x-10)=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/06 04:41:30
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1/(x-1)x+1/x(x+1)+.+1/(x+9)(x-10)=?
1/(x-1)x+1/x(x+1)+.+1/(x+9)(x-10)=?
1/(x-1)x+1/x(x+1)+.+1/(x+9)(x-10)=?
1/(X-1)X=1/(X-1)-1/X
1/X(X+1)=1/X-1/(X+1)
所以
原式=1/(X-1)-1/X+1/X-1/(X-1).-1/(X+10)
=1/(X-1)-1/(X+10)
1/(x-1)x
=1/x - 1/(x-1)
1/(x-1)x+1/x(x+1)+......+1/(x+9)(x-10)
=1/x - 1/(x-1)+1/(x+1)-1/x + ... + 1/(x-10)-1/(x+9)
= 1/(x-10)-1/(x-1)
x/x+(1-x)/x-1/x
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