How do you write the partial fraction decomposition of the rational expression (x^3 + x) /(x^2 + x + 1)^2x3+x(x2+x+1)2?

1 Answer
Sonnhard
May 25, 2018

(x^3+x)/(x^2+x+1)^2=(x-1)/(x^2+x+1)+(x+1)/(x^2+x+1)^2x3+x(x2+x+1)2=x−1x2+x+1+x+1(x2+x+1)2

Explanation:

Using the Ansatz
(x^3+x)/(x^2+x+1)^2=(Ax+B)/(x^2+x+1)^2+(Cx+D)/(x^2+x+1)x3+x(x2+x+1)2=Ax+B(x2+x+1)2+Cx+Dx2+x+1
we get A=1,B=-1,C=1,D=1A=1,B=−1,C=1,D=1

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