partial fraction decomposition of $\frac{{k}^{4}}{(a\phantom{\rule{thinmathspace}{0ex}}{k}^{3}-1{)}^{2}}$

I have to perform complex partial fraction decomposition of the following term:

$\frac{{k}^{4}}{(a\phantom{\rule{thinmathspace}{0ex}}{k}^{3}-1{)}^{2}}$

where $a$ is a real positive number.

and I would like to know if it is possible to reduce it to a sum of fractions of the type $\frac{A}{k\pm z}$,$\frac{B\phantom{\rule{thinmathspace}{0ex}}k}{{k}^{2}\pm z}$,$\frac{C\phantom{\rule{thinmathspace}{0ex}}k}{{k}^{2}-y}$ or similar. Where $z$ is a complex number and $y$ is a real number.

If it is not possible to reduce it to the kind of fraction I listed above other type of decomposition might work too.

Any hint on the process, or any reference would be nice.

Thanks in advance

I have to perform complex partial fraction decomposition of the following term:

$\frac{{k}^{4}}{(a\phantom{\rule{thinmathspace}{0ex}}{k}^{3}-1{)}^{2}}$

where $a$ is a real positive number.

and I would like to know if it is possible to reduce it to a sum of fractions of the type $\frac{A}{k\pm z}$,$\frac{B\phantom{\rule{thinmathspace}{0ex}}k}{{k}^{2}\pm z}$,$\frac{C\phantom{\rule{thinmathspace}{0ex}}k}{{k}^{2}-y}$ or similar. Where $z$ is a complex number and $y$ is a real number.

If it is not possible to reduce it to the kind of fraction I listed above other type of decomposition might work too.

Any hint on the process, or any reference would be nice.

Thanks in advance