已知x=√2+1,求(x+1/x^2-x-x/x^2-2x+1)÷1/x的值

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已知x=√2+1,求(x+1/x^2-x-x/x^2-2x+1)÷1/x的值
已知x=√2+1,求(x+1/x^2-x-x/x^2-2x+1)÷1/x的值

已知x=√2+1,求(x+1/x^2-x-x/x^2-2x+1)÷1/x的值
原式=[(x+1)/x(x-1)-x/(x-1)²]*x
=[(x+1)(x-1)-x²]/x(x-1)²*x
=(x²-1-x²)/x(x-1)²*x
=-1/x(x-1)²*x
=-1/(x-1)²
=-1/(√2+1-1)²
=-1/2