Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. \( \frac{3 x-2}{x\left(x^{2}+2\right)^{2}} \)

For the rational expression \( \frac{3 x-2}{x\left(x^{2}+2\right)^{2}} \), the partial fraction decomposition can be expressed as follows: \[ \frac{A}{x} + \frac{Bx + C}{x^2 + 2} + \frac{Dx + E}{(x^2 + 2)^2} \] Here, \( A \), \( B \), \( C \), \( D \), and \( E \) are constants that will be determined if you were to solve the equation. Each term corresponds to a factor in the denominator, appropriately handling the linear and squared requirements of the factors.