求助这道题怎么解？谢谢！

更新时间2019-02-01 11:13:58

[1/（1-x)-1/(1+x)]÷(x/(x²-1)+x]

=[(1+x)/(1-x²)-(1-x)/(1-x²)]÷[x(x²-1+1)/(x²-1)]

=2x/(1-x²)÷[x*x²/(x²-1)]

=-2/x²

∵x²/(x²-2)=1/(1-√3-√2)

∴(x²-2)/x²=1-√3-√2

则：1-2/x²=1-√3-√2

计：-2/x²=-√3-√2

所以：原式=-√3-√2

本题：x^2/(x^2-2)=1/(1-√3-√2)

x^2-x^2(√3+√2)=x^2-2

x^2=2/(√3+√2)

1/(1-x)-1/(1+x)÷[x/(x^2-1)+x)]

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

=2x/-(x^2-1)*[(x^2-1)/x(1+x^2-1)

=-2x/x^3

=-2/x^2

=-2/[2/(√3+√2)]

=-(√3+√2)

答案：本题的值为-(√3+√2)。

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