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

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 20:12:38

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

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

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

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