Question

Consider the decomposition of

(6x^3+x−3)/(x^2−2x+1)

Answer 1

$$\dfrac{6x^3+x-3}{x^2-2x+1}=\dfrac{6x(x^2-2x+1)+12x^2-6x+x-3}{x^2-2x+1}$$

$$=6x+\dfrac{12(x^2-2x+1)+24x-12-5x-3}{x^2-2x+1}$$

$$=6x+12+\dfrac{19(x-1)+19-15}{(x-1)^2}$$

$$=6x+12+\dfrac{19}{(x-1)}+\dfrac{4}{(x-1)^2}$$