化简求值:(x2-4/x2+x+1)2/(x3-3x2+2x/x3-1)2*(x/x+2).其中x=-2/3
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[(x^2-4)/(x^2+x+1)]^2
=[(x+2)(x-2)/(x^2+x+1)]^2
=(x+2)^2(x-2)^2/(x^2+x+1)^2
[(x^3-3x^2+2x)/(x^3-1)]^2
=[x(x^2-3x+2)/(x^3-1)]^2
=[x(x-2)(x-1)/(x-1)(x^2+x+1)]^2
=x^2(x-2)^2(x-1)^2/(x-1)^2(x^2+x+1)^2
(x2-4/x2+x+1)2/(x3-3x2+2x/x3-1)2*(x/x+2)
=(x+2)^2(x-2)^2/(x^2+x+1)^2*(x-1)^2(x^2+x+1)^2/x^2(x-2)^2(x-1)^2*(x/x+2)
=(x+2)/x
=(-2/3+2)*(-3/2)
=4/3*(-3/2)
=-2
=[(x+2)(x-2)/(x^2+x+1)]^2
=(x+2)^2(x-2)^2/(x^2+x+1)^2
[(x^3-3x^2+2x)/(x^3-1)]^2
=[x(x^2-3x+2)/(x^3-1)]^2
=[x(x-2)(x-1)/(x-1)(x^2+x+1)]^2
=x^2(x-2)^2(x-1)^2/(x-1)^2(x^2+x+1)^2
(x2-4/x2+x+1)2/(x3-3x2+2x/x3-1)2*(x/x+2)
=(x+2)^2(x-2)^2/(x^2+x+1)^2*(x-1)^2(x^2+x+1)^2/x^2(x-2)^2(x-1)^2*(x/x+2)
=(x+2)/x
=(-2/3+2)*(-3/2)
=4/3*(-3/2)
=-2
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