For the following function I need the approach for partial fraction decomposition?

Approach:

(-x4 + 2×3 – 3×2 + 4x – 5) / ((x – 3)2 * (x + 1) * x3) =

(A / x) + (B / x2) + (C / x3) + (D / (x – 3)) + (E / (x – 3)2) + (F / (x + 1))

You take this to the main necessary ((x – 3)2 * (x + 1) * x3), multiply the clamps, sort by ascending potencies of x and clamp the coefficients A – F before the potencies.

With the coefficients, you make a coefficient comparison with the original counter of the polynomial and set a equation system to determine the coefficients A – F.

You realize it’s not that easy, it’s definitely a lot of computational effort.

(-x4 + 2×3 – 3×2 + 4x – 5) / ((x – 3)2 * (x + 1) * x3) =

((-23 / 27) / x) + ((17 / 27) / x2) + ((-5 / 9) / x3) + ((-37 / 432) / (x – 3)) + ((-47 / 108) / (x – 3)2) + ((15 / 16) / (x + 1))