# How do you write the partial fraction decomposition of the rational expression (x^3 + x) /(x^2 + x + 1)^2?

$\frac{{x}^{3} + x}{{x}^{2} + x + 1} ^ 2 = \frac{x - 1}{{x}^{2} + x + 1} + \frac{x + 1}{{x}^{2} + x + 1} ^ 2$
$\frac{{x}^{3} + x}{{x}^{2} + x + 1} ^ 2 = \frac{A x + B}{{x}^{2} + x + 1} ^ 2 + \frac{C x + D}{{x}^{2} + x + 1}$
we get $A = 1 , B = - 1 , C = 1 , D = 1$