Question on Partial Fractions

Merry Christmas everyone!

I would be very grateful if someone could take the time out to help me with this partial fractions problem:



I have been able to do the first part. However, I haven't been able to use that first part to express the given statement in partial fractions. The following are my workings: Could you please tell me if I have approached that part of the question correctly or is there another method to arrive at the required answer?







Also, in case this helps - here is the answer I must arrive it:



I made some progress but am not sure what to do thereafter.

Thank you all very much!

the first part is correct

after this is just irreducible quadratic partial fractions.
they are written correctly
So patience, focus and concentration.
(this is the purpose of this exercise)

Is this step correct? Is this the right method to work on irreducible quadratic partial fractions (cos I'm not sure)? So, it is basically just solving for A,B,C & D in that case?

Thank you!