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通分：(1)x/x^2+2x+1,(2)x-1/x^2+x,(3)1/x^2-1

分类: 作业答案 • 2021-12-20 08:45:24
问题描述：

通分：(1)x/x^2+2x+1,(2)x-1/x^2+x,(3)1/x^2-1

答

x/(x^2+2x+1)
=x/(x+1)^2
=x^2(x-1)/[x(x+1)^2(x-1)]
=(x^3-x^2)/[x(x+1)^2(x-1)]
(x-1)/(x^2+x)
=(x-1)/[x(x+1)]
=(x-1)^2(x+1)//[x(x+1)^2(x-1)]
=(x^3-x^2-x+1)/[x(x+1)^2(x-1)]
1/(x^2-1)
=1/[(x+1)(x-1)]
=x(x+1)/[x(x+1)^2(x-1)]
=(x^2+x)/[x(x+1)^2(x-1)]

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