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Need help with partial fraction

Attachment 20743

I get stuck at the ((Ax+B)/(x^2+1)) + ((Cx+D)/(x^2+2)) part.

How exactly do we solve for these variables A, B, C, and D? If I plug in zero the equation would become:

3x^3 - x^2 + 6x - 4 = (Ax+B)(x^2+2) + (Cx+D)(x^2+1)

3(0)^3 - (0)^2 + 6(0) - 4 = (A(0)+B)((0)^2+2) + (C(0)+D)((0)^2+1)

That would leave me with: -4 = 2B + D.

I have tried multiplying it out and setting it equal to the coefficient such as this:

A + C = 3

B + D = -1

2A + C = 6

2B + D = -4

But to no avail. Please help me figure out how to solve for these variables. Thanks in advance.