Partial fractions question

[aname]

I am having problems with this question

3. \(\displaystyle \dfrac{1}{w^4\, -\, w^3}\)

I know I have to use partial fractions, and I got to this point

1 = A(x^2)(x-1) + B(x)(x-1) - (x)(x-1) + (x^3)

I trie plugging in x = 2 and x = -1 into the equation above to solve for A and B, but I keep getting the wrong answers for A and B?

The equations I end up with after plugging in x = 2 and x = -1 are
-5 = 4A + 2B and
4 = -2A + 2B, respectively, giving me

A = -3/2 and B = 1/2, but apparently A and B = -1?

Am I doing something wrong?

 

[aname]

Oh, I see my mistake now, I wrote (x)(x-1) twice. I'll correct it and let you know how it goes.

 

[aname]

After correcting my mistake, I got the right answer.

Would anyone like to see the process? It might take a while for me to post up though, since all my finals this quarter are grouped on Monday and Tuesday.

 

[stapel]

Would anyone like to see the process?

The steps you took could be very helpful for other students, so please feel free, as time allows, to post. (Note: To avoid confusion, it would probably be useful to stick to the variable "w". Switching to "x" could be befuddling.) Thank you!