express the following in terms of partial fraction:
2/(1+x+x2+x3)
thanks~
pure maths
2009-09-07 5:49 am
回答 (1)
2009-09-07 5:53 am
✔ 最佳答案
Note that x3 + x2 + x + 1 = (x + 1)(x2 + 1)We let 2/(x3 + x2 + x + 1) = A / (x + 1) + (Bx + C) / (x2 + 1)
2 = (A + B)x2 + (B + C)x + (A + C)
Comparing coefficients,
A + B = 0, A = -B
B + C = 0, B = -C
So, A = C
A + C = 2, A = C = 1
B = -1
2/(x3 + x2 + x + 1) = 1/(x + 1) + (-x + 1)/(x2 + 1)
參考: Physics king
收錄日期: 2021-04-19 15:18:01
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