SOLUTION: I am finding partial decomposition very intimidating-Please help if you can:)Thank You very much! Find the unknowns on the right side of the partial fraction decomposition. x+3/

Question 137356: I am finding partial decomposition very intimidating-Please help if you can:)Thank You very much!
Find the unknowns on the right side of the partial fraction decomposition.
x+3/x^3+64=A/x=4+Bx+C/x^2-4x+16
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the unknowns on the right side of the partial fraction decomposition.
(x+3)/(x^3+64) = (x+3)/[(x+4)(x^2-4x+16)
(x+3)/(x^3+64) = A/(x+4) + (Bx+C)/(x^2-4x+16)
The denominators are the same so just work with the numerators:
x+3 = A(x^2-4x+16) + (Bx+C)(x+4)
x+3 = Ax^2-4Ax+16A + Bx^2+4Bx + Cx + 4C
x+3 = (A+B)x^2 + (4B-4A+C)x + (16A +4C)
----------------
EQUATIONS:
A + B + 0 = 0
-4A +4B + C = 1
16A +0 +4C = 3
--------------------
Solving for A, B, and C you get:
A = -1/48
B = 1/48
C = 40/48
=======================
Cheers,
Stan H.
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