Answer
$\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{Cx+D}{x^2+4}+\dfrac{Ex+F}{(x^2+4)^2}$
Work Step by Step
Simplify $\dfrac{x^4+x^2+1}{x^2(x^2+4)^2}$ into partial fraction decomposition.
Here, the denominator terms can be be further factorized.Thus, the partial decomposition will be shown in a linear function of $x$.
Applying the partial fraction decomposition rule.
$\dfrac{x^4+x^2+1}{x^2(x^2+4)^2}=\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{Cx+D}{x^2+4}+\dfrac{Ex+F}{(x^2+4)^2}$