Question 137356
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.