已知X²＋X－1=0，求X[(1－2/(1－X)÷(X＋1)－(X²－1)/(X²－2X＋1)的值 要过程
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X²＋X－1=0
X²＋X = 1
X[(1 - 2/(1-X) ] ÷ [(X+1) - (X²-1)/(X²-2X+1)]
=X[(1-X-2)/(1-X) ] ÷ [(X+1)-(X+1)(X-1)/(X-1)²]
=X[(-X-1)/(1-X) ] ÷ [(X+1)-(X+1)/(X-1)]
=X[-(X+1)/(1-X) ] ÷ [(X+1)(X-1)-(X+1)]/(X-1)
=X[(X+1)/(X-1) ] ÷ [X²-1-X-1)]/(X-1)
=X[(X+1)/(X-1) ] ÷ [X²-X-2)]/(X-1)
=X[(X+1)/(X-1) ] ÷ (X+2)
=X(X+1) / [(X-1)(X+2)]
=(X^2+X) / (X^2+X-2)
=1/(1-2)
=-1
X²＋X = 1
X[(1 - 2/(1-X) ] ÷ [(X+1) - (X²-1)/(X²-2X+1)]
=X[(1-X-2)/(1-X) ] ÷ [(X+1)-(X+1)(X-1)/(X-1)²]
=X[(-X-1)/(1-X) ] ÷ [(X+1)-(X+1)/(X-1)]
=X[-(X+1)/(1-X) ] ÷ [(X+1)(X-1)-(X+1)]/(X-1)
=X[(X+1)/(X-1) ] ÷ [X²-1-X-1)]/(X-1)
=X[(X+1)/(X-1) ] ÷ [X²-X-2)]/(X-1)
=X[(X+1)/(X-1) ] ÷ (X+2)
=X(X+1) / [(X-1)(X+2)]
=(X^2+X) / (X^2+X-2)
=1/(1-2)
=-1
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