How do you express ((x^3+1)/(x^2+3)) in partial fractions?

$\frac{{x}^{3} + 1}{{x}^{2} + 3} = x - \frac{3 x - 1}{{x}^{2} + 3}$
${x}^{3} + 1 = x \left({x}^{2} + 3\right) - 3 x + 1$
Hence, $\frac{{x}^{3} + 1}{{x}^{2} + 3} = x + \frac{- 3 x + 1}{{x}^{2} + 3}$ or $x - \frac{3 x - 1}{{x}^{2} + 3}$
As ${x}^{2} + 3$ cannot be factorized, you cannot have further partial fractions.