Decompose: 5/[x(x + 2)]?
- 1/x + 4/(x + 2)
- 3/x+2/(x + 2)
- 5/(2x) + - 5/[2(x + 2)]
- None of these
Explanation
5/[x(x + 2)] = A/x + B/(x + 2)
Multiply both sides by x(x + 2)
5 = A(x + 2) + Bx
Put x = 0
5 = A(0 + 2) + B×0
5 = 2A
A = 5/2
Put x = -2
5 = A(-2 + 2) + B(-2)
5 = -2B
B = -5/2
So 5/[x(x + 2)] = 5/(2x) - 5/[2(x + 2)]
Last verified on 04-05-2026
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