Answer
$\displaystyle \frac{x^{4}+x^{3}-x^{2}+x-1}{x^{3}(x^{2}+1)}$
Work Step by Step
Both denominators are irreducible.
LCD = $x^{3}(x^{2}+1)$
$\displaystyle \frac{x-1}{x^{3}}+\frac{x}{x^{2}+1}=\frac{(x-1)(x^{2}+1)+x\cdot x^{3}}{x^{3}(x^{2}+1)}$
$=\displaystyle \frac{(x^{3}+x-x^{2}-1)+x^{4}}{x^{3}(x^{2}+1)}$
$=\displaystyle \frac{(x^{3}+x-x^{2}-1)+x^{4}}{x^{3}(x^{2}+1)}$
$=\displaystyle \frac{x^{4}+x^{3}-x^{2}+x-1}{x^{3}(x^{2}+1)}$
