Question

已知x^2+x-1=0,求x(1-2/1-x )÷(x+1)- x(x^2-1)/x^2-2x+1

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Answer 1

∵x²+x-1=0
∴x²=1-x
x(1-2/1-x )÷(x+1)- x(x²-1)/(x²-2x+1)
=x(1-x-2)/(1-x)*1/(x+1)-x(x-1)(x+1)/(x-1)²
=x(-x-1)/(1-x)(x+1)-x(x+1)/(x-1)
=x/(x-1)-(x²+x)/(x-1)
=(x-x²-x)/(x-1)
=-x²/(x-1)
=-(1-x)/(x-1)
=(x-1)/(x-1)
=1