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解：
令x^(1/3)=t，则x=t^3
(x-1)/[x^(2/3)+x^(1/3)+1]+(x+1)/[x^(1/3)+1]-[x-x^(1/3)]/[x^(1/3)-1]
=(t^3-1)/(t^2+t+1)+(t^3+1)/(t+1)-(t^3-t)/(t-1)
=(t-1)(t^2+t+1)/(t^2+t+1)+(t+1)(t^2-t+1)/(t+1)-t(t+1)(t-1)/(t-1)
=t-1+t^2-t+1-t^2-t
=-t
=-x^(1/3)
令x^(1/3)=t，则x=t^3
(x-1)/[x^(2/3)+x^(1/3)+1]+(x+1)/[x^(1/3)+1]-[x-x^(1/3)]/[x^(1/3)-1]
=(t^3-1)/(t^2+t+1)+(t^3+1)/(t+1)-(t^3-t)/(t-1)
=(t-1)(t^2+t+1)/(t^2+t+1)+(t+1)(t^2-t+1)/(t+1)-t(t+1)(t-1)/(t-1)
=t-1+t^2-t+1-t^2-t
=-t
=-x^(1/3)
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