(x^4+3x^3+5x^2+7x+9)/(x^2+2)

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(x^4+3x^3+5x^2+7x+9)/(x^2+2)
(x^4+3x^3+5x^2+7x+9)/(x^2+2)

(x^4+3x^3+5x^2+7x+9)/(x^2+2)
(x^4+3x^3+5x^2+7x+9)/(x^2+2)
=x^2+3x+3+(7x+3)/(x^+2)

(x^4+3x^3+5x^2+7x+9)/(x^2+2)
=(x^4+2x^2+3x^3+6x+3x^2+6+x+3)/(x^2+2)
=(x^2+3x+3) +(x+3)/(x^2+2)

(x^4+3x^3+5x^2+7x+9)/(x^2+2)
=[(x^4+4x^2+4)+(x^2+2)+3x(x^2+2)+(x+3)]/(x^2+2)
=(x^2+2)^2/(x^2+2)+(x^2+2)/(x^2+2)+3x(x^2+2)/(x^2+2)+(x+3)/(x^2+2)
=x^2+2+1+3x+(x+3)/(x^2+2)
=x^2+3x+3+(x+3)/(x^2+2).

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