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

Feb 15, 2016

Partial fractions of ${x}^{2} / \left({x}^{2} + x + 2\right)$ are 1-(x+2)/(x^2+x+2

#### Explanation:

As the denominator ${x}^{2} + x + 2$ is quadratic and its determinant $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ is not rational (as $\sqrt{{b}^{2} - 4 a c} = \sqrt{- 7}$ is not rational), its partial fractions will be of type $\frac{A x + B}{{x}^{2} + x + 2}$.

But, degree of numerator is $2$ hence let us write ${x}^{2} / \left({x}^{2} + x + 2\right)$ as

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

Hence partial fractions of ${x}^{2} / \left({x}^{2} + x + 2\right)$ are 1-(x+2)/(x^2+x+2