Answer
$\dfrac{Ax+B}{x^2+1}+\dfrac{Cx+D}{x^2+2}$
Work Step by Step
Simplify $\dfrac{x^3-4x^2+2}{(x^2+1)(x^2+2)}$ 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.
$\dfrac{x^3-4x^2+2}{(x^2+1)(x^2+2)}=\dfrac{Ax+B}{x^2+1}+\dfrac{Cx+D}{x^2+2}$
