(-3x^6 +9x^5 -12x^4 +18x^3 -22x^2 +14x -6)/(x^4 -3x^3 +4x^2 -3x +1)

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(-3x^6 +9x^5 -12x^4 +18x^3 -22x^2 +14x -6)/(x^4 -3x^3 +4x^2 -3x +1)

`-3x^6+9x^5-12x^4+18x^3-22x^2+14x-6`

`=-3x^6+9x^5-12x^4+9x^3+9x^3-3x^2-19x^2+14x-6`

`=-3x^2(x^4-3x^3+4x^2-3x+1)+9x^3-19x^2+14x-6`

`Thus`

`(-3x^6+9x^5-12x^4+18x^3-22x^2+14x-6)/(x^4-3x^3+4x^2-3x+1)`

`=(-3x^2(x^4-3x^3+4x^2-3x+1)+(9x^3-19x^2+14x-6))/(x^4-3x^3+4x^2-3x+1)`

`=(-3x^2(x^4-3x^3+4x^2-3x+1))/(x^4-3x^3+4x^2-3x+1)+(9x^3-19x^2+14x-6)/(x^4-3x^3+4x^2-3x+1)`

`=-3x^2+(9x^3-19x^2+14x-6)/(x^4-3x^3+4x^2-3x+1)`

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