TS EAMCET · Maths · Basic of Mathematics
If \(\frac{3 x+1}{(x-1)^2\left(x^2+1\right)}=\frac{\mathrm{A}}{x-1}+\frac{\mathrm{B}}{(x-1)^2}+\frac{\mathrm{C} x+\mathrm{D}}{x^2+1}\), then \(2(\mathrm{~A}-\mathrm{C}+\mathrm{B}+\mathrm{D})=\)
- A 0
- B 1
- C 2
- D -1
Answer & Solution
Correct Answer
(D) -1
Step-by-step Solution
Detailed explanation
Let the given equation be \(3x+1 = \mathrm{A}(x-1)(x^2+1) + \mathrm{B}(x^2+1) + (\mathrm{C}x+\mathrm{D})(x-1)^2\) Set \(x=1\): \(3(1)+1 = \mathrm{A}(0) + \mathrm{B}(1^2+1) + (\mathrm{C}(1)+\mathrm{D})(0)^2\) \(4 = 2\mathrm{B} \implies \mathrm{B}=2\) Expand and equate…
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