Partial fraction decomposition of 1/(x²-1)²

[opus]

Homework Statement

Find the partial fraction decomposition for:

$\frac{1}{\left(x^2-1\right)^2}$

Homework Equations

The Attempt at a Solution

Please see my attached images. I think the image shows my thought process better and it would take me well over an hour to type all that out!

Im stuck at the very end, where it results in a true statement, yet I'm trying to get values for A and C (Step iv-c)

 

[opus]

Please see attached. The second image is Page 1.

 

[Stephen Tashi]

Try solving the simultaneous equations
$-A - 2B - C + 2D = 0$
$A + B - C + D = 1$
instead of the two you choose.

If you add the two equations you choose, you can see that $A$ and $C$ are eliminated from the result, which suggests the two you selected don't provide information about the individual values of $A$ and $C$.

 

[opus]

Great thank you!