SOLUTION: I'm really stuck on solving this partial fraction: 3/x(x+17)(x^2+13)= A/x+B/x+17+Cx+D/x^2+13

Question 447150: I'm really stuck on solving this partial fraction:
3/x(x+17)(x^2+13)= A/x+B/x+17+Cx+D/x^2+13

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I'm really stuck on solving this partial fraction:
3/x(x+17)(x^2+13)= A/x + B/(x+17) + (Cx+D)/(x^2+13)
---
Multiply thru by x(x+17)(x^2+13)
-------------------
0x^3 + 0x^2 + 0x + 3 = A(x+17)(x^2+13) + B(x)(x^2+13) + (Cx+d)x(x+17)
--------------------------------------------------------------------
0x^3+0x^2+0x+3 = A[x^3+17x^2+13x+221]+ B[x^3+13x] + [Cx^3+17Cx^2+Dx^2+17Dx]
--------------------------------------------------
0x^3+0x^2+0x+3 = A[x^3+17x^2+13x+221]+ B[x^3+13x]+C[x^3+17x^2]+D[x^3+17x]
-----------------------------------------------------
X^3:::: A + B + C + D = 0
x^2:: 17A + 0B + 17C + 0 = 0
x::: 13A + 13B + 0C +17D = 0
-::: 221A + 0B + 0C + 0D = 3
----------------------------------------
Comment: Above is the process. You'll have to
check the math.
Cheers,
Stan H.
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