(8x + 6)/x(x + 2) decomposes as?
- 3/x + 5/(x+2)
- 4/x + 5/(x+2)
- 5/x + 5/(x+2)
- None of these
Explanation
The decomposition is:
(8x + 6)/[x(x + 2)] = A/x + B/(x + 2)
Multiply both sides by x(x + 2) so the denominators cancel out:
8x + 6 = A(x + 2) + Bx
Now find A and B:
Put x = 0. That makes the Bx term zero, so 6 = 2A. That gives A = 3.
Put x = -2. That makes the A(x + 2) term zero, so -10 = -2B. That gives B = 5.
So it equals 3/x + 5/(x + 2).
Last verified on 15-05-2026
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