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分式化简：（1）1/x-1/(X+1) (2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)
题目详情
分式化简：（1）1/x-1/(X+1) (2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)
▼优质解答
答案和解析
（1）1/x-1/(x+1)=（x+1-x）/（x（x+1））=1/(x(x+1))
(2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)
=1/x-1/(x+1）+1/(x+1)-1/(x+2)+……+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)
=(x+1000-x)/(x(x+1000))
=1000/(x(x+1000))
(2)1/x(x+1)+1/(X+1)(x+2)+...+1/（x+999)(x+1000)
=1/x-1/(x+1）+1/(x+1)-1/(x+2)+……+1/(x+999)-1/(x+1000)
=1/x-1/(x+1000)
=(x+1000-x)/(x(x+1000))
=1000/(x(x+1000))
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