Question

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

Answer 1

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

Explanation:

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)`