1/(x-1)x+1/x(x+1)+......+1/(x+9)(x-10)=？ 请详细说出解题过程，谢谢
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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(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)
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展开全部
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)
=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)
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