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x^2+x+1/x^2+1/x–4
=x^2+x–4+1/x+1/x^2
=(x^4+x^3-4x^2+x+1)/x^2
=(x^4-x^3+2x^3-2x^2-2x^2+2x-x+1)/x^2
=[(x^4-x^3)+(2x^3-2x^2)-(2x^2-2x)-(x-1)]/x^2
=[x^3(x-1)+2x^2(x-1)-2x(x-1)-(x-1)]/x^2
=(x-1)(x^3+2x^2-2x-1)/x^2
=x^2+x–4+1/x+1/x^2
=(x^4+x^3-4x^2+x+1)/x^2
=(x^4-x^3+2x^3-2x^2-2x^2+2x-x+1)/x^2
=[(x^4-x^3)+(2x^3-2x^2)-(2x^2-2x)-(x-1)]/x^2
=[x^3(x-1)+2x^2(x-1)-2x(x-1)-(x-1)]/x^2
=(x-1)(x^3+2x^2-2x-1)/x^2
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