Question

How do you express `x^2/(x^2 + x +2)` in partial fractions?

Answer 1

Partial fractions of `x^2/(x^2+x+2)` are `1-(x+2)/(x^2+x+2`

Explanation:

As the denominator `x^2+x+2` is quadratic and its determinant `(-b+-sqrt(b^2-4ac))/(2a)` is not rational (as `sqrt(b^2-4ac)=sqrt(-7)` is not rational), its partial fractions will be of type `(Ax+B)/(x^2+x+2)`.

But, degree of numerator is `2` hence let us write `x^2/(x^2+x+2)` as

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

Hence partial fractions of `x^2/(x^2+x+2)` are `1-(x+2)/(x^2+x+2`