Answer
$$\frac{{Ax + B}}{{{x^2} + 5}} + \frac{{Cx + D}}{{{{\left( {{x^2} + 5} \right)}^2}}}$$
Work Step by Step
$$\eqalign{
& {\text{Given exercise }}\frac{{4{x^3} - x}}{{{{\left( {{x^2} + 5} \right)}^2}}} \cr
& {\text{In the denominator the expression is }}{\left( {{x^2} + 5} \right)^2}{\text{ it is a quadratic}} \cr
& {\text{repeated factor, then the numerator for each term of the partial}} \cr
& {\text{decomposition introduce in the numerator one terms of the form}} \cr
& {\text{linear }}Ax + B{\text{ and }}Cx + D,{\text{ the partial decomposition is:}} \cr
& \frac{{4{x^3} - x}}{{{{\left( {{x^2} + 5} \right)}^2}}} = \frac{{Ax + B}}{{{x^2} + 5}} + \frac{{Cx + D}}{{{{\left( {{x^2} + 5} \right)}^2}}} \cr} $$
