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x^2+x+1/x^4+x^2+1=x^2+x+1/x^4+2*x^2+1-x^2=x^2+x+1/(x^2+1)-x^2=x^2+x+1/(x^2-x+1)*(x^2+x+1)=1/x^2-x+1
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x^2+x+1/x^4+x^2+1=x^2+x+1/x^4+2*x^2+1-x^2=x^2+x+1/(x^2+1)-x^2=x^2+x+1/(x^2-x+1)*(x^2+x+1)=1/x^2-x+1