(5x + 3)/(x(x + 1) decomposes as?
- 4/x + 1/(x + 1)
- 1/x + 4/(x + 1)
- 3/x + 2/(x + 1)
- None of these
Explanation
Problem: (5x + 3)/(x(x + 1))
Step 1: Set up
(5x + 3)/(x(x + 1)) = A/x + B/(x + 1)
Step 2: Find A
Put x = 0 in (5x + 3)/(x + 1)
(5_0 + 3)/(0 + 1) = 3/1 = 3
So A = 3
Step 3: Find B
Put x = -1 in (5x + 3)/x
(5_-1 + 3)/(-1) = (-5 + 3)/(-1) = -2/-1 = 2
So B = 2
Answer: 3/x + 2/(x + 1)
Last verified on 08-05-2026
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