Question

Decompose in partial fractions in R[X] and in C[X]:

Answer 1

\[X ^{7}/(X ^{2}+1)^{2}(X−1)\]

Answer 2

First write the partial fractions over the reals. That's a high-school level problem.

Then once you have that, to find the decomposition over the complex numbers, break up the terms with denominators in multiples of (x^2+1) into terms with (x+i) and (x-i)

Answer 3

thanks JamesJ. ive done what you said, and got

5/4(x+i)(x-i) + 1/4(x-1) - 1/(x-i)^2(x+i)^2

do i need to do anything further?