Mathematics: Partial Fractions

[Mansize_tissue]

'Any maths guys in here who want to give me a hand?

Express the following as a sum of partial fractions:

(x^2 - 1)/(x^2)(2x + 1)


Here's what I've done:

(x^2 - 1)/(x^2)(2x + 1) = A/(2x + 1) + B/x + C/x^2

So...

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

From there, by substituting x = -0.5, I got A = 6
Then I equated the coefficients and got B = -3 and C = 2

However, apparently this is incorrect and I can't work out where I've gone wrong. Any help?

 

[Mansize_tissue]

That's what I thought, >:|sh4d0w|:<.

However, this is the answer in the book:

2/x - 1/x^2 - 3/(2x + 1)

So there are 3 separate fractions, apparently. This doesn't make any sense.

Thank you for the prompt reply, by the way.

 

[Mansize_tissue]

Oh, I see now. Both methods work I think, I was just doing it the very long way. The reason my method didn't work I think was because I needlessly multiplied each term by x when I didn't have to in order to make the denominators the same.

Thank you very much for your help.

However, I'm going to have to be picky:

When x = 0; -1 = Ax+B (1)

If x = 0 won't Ax = 0?

 

[Mansize_tissue]

Thank you for all the help guys, I really appreciate it.