How do you write the partial fraction decomposition of the rational expression $x^2 /(x^2 +x+2)$ ?

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Answer 1 · 2016-08-12T21:42:53

$x^2/(x^2+x+2)=1-(x+2)/(x^2+x+2)$

Note that the discriminant of $x^2+x+2$ is negative, so it has no Real zeros.

So unless we want a partial fraction decomposition with Complex coefficients, the best we can do is:

$x^2/(x^2+x+2)=((x^2+x+2)-(x+2))/(x^2+x+2)=1-(x+2)/(x^2+x+2)$

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