已知x²+3x-1=0,求(x-3)/(3x²-6x)÷（x+2-5/(x+2)）的值

已知x²+3x-1=0,求(x-3)/(3x²-6x)÷（x+2-5/(x+2)）的值
已知x²+3x-1=0,求(x-3)/(3x²-6x)÷（x+2-5/(x+2)）的值

已知x²+3x-1=0,求(x-3)/(3x²-6x)÷（x+2-5/(x+2)）的值
x²+3x-1=0
x²+3x=1
(x-3)/3x²-6x）/[(x+2-5/(x-2)]
={(x-3)/[3x(x-2)]}/{[(x+2)(x-2)-5]/(x-2)]}
={(x-3)/[3x(x-2)]}/[(x²-9)/(x-2)]
={(x-3)/[3x(x-2)]}/{[(x+3)(x-3)]/(x-2)]}
=1/[3x(x+3)]
=1/[3(x²+3x)]
=1/3

因为x²+3x-1=0
那么x²+3x=1
(x-3/3x^2-6x）/（x+2-5/x-2)
={(x-3)/[3x(x-2)]}/{[(x+2)(x-2)-5]/(x-2)]}
={(x-3)/[3x(x-2)]}/[(x²-9)/(x-2)]
={(x-3)/[3x(x-2)]}/{[(x+3)(x-3)]/(x-2)]}
=1/[3x(x+3)]
=1/[3(x²+3x)]
=1/3

原式=(x-3)/(3x²-6x)÷[x+2-5/(x-2)]
=(x-3)/3x(x-2)÷[(x^2-9)/(x-2)]
=(x-3)/3x(x-2)×(x-2)/(x^2-9)
=(x-3)/3x(x-2)×(x-2)/(x-3)(x+3)
...

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原式=(x-3)/(3x²-6x)÷[x+2-5/(x-2)]
=(x-3)/3x(x-2)÷[(x^2-9)/(x-2)]
=(x-3)/3x(x-2)×(x-2)/(x^2-9)
=(x-3)/3x(x-2)×(x-2)/(x-3)(x+3)
=1/3x(x+3)
=1/3(x^2+3x) 由x^2+3x-1=0得x^2+3x=1
=1/3

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