Partial Fraction Decomposition

[protivakid]

Homework Statement

\frac{4x^{4}-8x^{3}+5x^{2}-2x-1}{2x^{2}-3x-2}

Homework Equations

The Attempt at a Solution

I started of by breaking the bottom part down into (2x+1)(x-2) which then allowed me to set...
\frac{A}{(2x+1)}+\frac{B}{(x-2)}

The problem is from here I tried synthetic division however it gave me an answer that did not make any sense. Am I setting this up right or have I messed up already? Thanks guys.

 

[Defennder]

I don't know if you forgot to include the step of dividing the polynomial fraction such that the degree of the numerator polynomial is less than that of the denominator's.

 

[protivakid]

Thanks for the reply, I didn't forget to put it in, I forgot to do it lol. I'm still learning how to do all these problems so even obvious hints make a world of difference to me. I managed to completely solve it from there so thank you.