partial fraction decomposition

Question

x+6 ÷x²(x²+2)

Answer 1

(x+6) / [x²(x²+2)] = A/x + B/x² + (Cx+D)/(x²+2)

So, x + 6 = Ax(x²+2) + B(x²+2) + (Cx+D)x²

0x³ + 0x² + x + 6 = (A+C)x³ + (B+D)x² + (2A)x + (2B)

So, A+C = 0, B+D = 0, 2A = 1, and 2B = 6

Thus, A = 1/2, B = 3, C = -1/2, and D = -3

(x+6) / [x²(x²+2)] = 1/(2x) + 3/x² - x/(2x²+ 4) - 3/(x²+2)