I'd be very grateful if someone could help me with this problem. My math book does a horrific job of explaining this partial fraction decomposition stuff. Thanks a million!
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(9x + 1)/(x^3 + x²) = (9x + 1)/(x²)(x + 1) = (Ax + B)/(x²) + C/(x + 1)
(x + 1)(Ax + B) + C(x²) = 9x + 1
When x = 0:
B = 1
When x = -1:
C = -8
When x = 1:
2A - 6 = 10 --> A = 8
Therefore:
(9x + 1)/(x^3 + x²) = (8x + 1)/(x²) - 8/(x + 1)
(x + 1)(Ax + B) + C(x²) = 9x + 1
When x = 0:
B = 1
When x = -1:
C = -8
When x = 1:
2A - 6 = 10 --> A = 8
Therefore:
(9x + 1)/(x^3 + x²) = (8x + 1)/(x²) - 8/(x + 1)