Answer
$ \dfrac{x^4+x^3-x^2+x-1}{x^3(x^2+1)}$
Work Step by Step
Since the least common multiple (LCM) of the denominator is $x^3(x^2+1)$, then we have
$$
\frac{x-1}{x^3}+\frac{x}{x^2+1}=\frac{(x-1)(x^2+1)}{x^3(x^2+1)}+\frac{x^4}{x^3(x^2+1)}
.$$
Now, since the denominators are the same, then we have
$$
\frac{(x-1)(x^2+1)}{x^3(x^2+1)}+\frac{x^4}{x^3(x^2+1)}= \frac{x^4+x^3-x^2+x-1}{x^3(x^2+1)}
.$$
