Question

I'm trying to find the partial fraction decomposition of:

10x^2+2x-2/x^2(x+1)

I already found B=-2 and C=6

Plugging in the numbers, I get:

10x^2+2x-2=Ax(x+1)+(-2)(x+1)+(6)x^2

How do I solve this for A? Maybe this is just some algebra that I'm rusty on. But I'm having trouble with this. Help please?

Answer 1

so far, so good. You now have
10x^2+2x-2 = Ax(x+1)+(-2)(x+1)+(6)x^2
10x^2+2x-2 = Ax^2+Ax-2x-2+6x^2
10x^2+2x-2 = (A+6)x^2 - (A-2)x - 2
for those two polynomials to be identical, all the coefficients must match. That is

A+6 = 10
A-2 = 2
So, A=4
Luckily, those two equations give the same solution for A. I'm just curious how you found B and C without seeing how to get A. B I can see, since you wound up with

(A+C)x^2 + (A+B)x + B

Answer 2

To get B, I plugged in A=0. To get C I plugged in B=-1

Answer 3

No, I plugged in X=0 and X=-1