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

${x}^{2} / \left({x}^{2} + x + 2\right) = 1 - \frac{x + 2}{{x}^{2} + x + 2}$
Note that the discriminant of ${x}^{2} + x + 2$ is negative, so it has no Real zeros.
${x}^{2} / \left({x}^{2} + x + 2\right) = \frac{\left({x}^{2} + x + 2\right) - \left(x + 2\right)}{{x}^{2} + x + 2} = 1 - \frac{x + 2}{{x}^{2} + x + 2}$