已知x=根号2+1,求x+1-x-1分子x平方

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已知x=根号2+1,求x+1-x-1分子x平方

原式=(x+1)-x²/(x-1)
=[(x²-1)-x²]/(x-1)
=-1/(x-1)
而x=√2+1
∴x-1=√2
即原式=-1/√2=-√2/2

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