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AP EAMCET · Maths · Basic of Mathematics

If \(\frac{3 x+1}{(x-1)\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^2+2}\), then \(5(A-B)=\)

  1. A \(\mathrm{A}+\mathrm{C}\)
  2. B \(8 C\)
  3. C \(\mathrm{C}+8\)
  4. D \(\frac{C}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(8 C\)

Step-by-step Solution

Detailed explanation

\(3x+1 = A(x^2+2) + (Bx+C)(x-1)\) Set \(x=1\): \(4 = A(1^2+2) \Rightarrow 4 = 3A \Rightarrow A=\frac{4}{3}\) Coeff of \(x^2\): \(0 = A+B \Rightarrow B = -A = -\frac{4}{3}\) Coeff of constant: \(1 = 2A-C \Rightarrow C = 2A-1 = 2(\frac{4}{3})-1 = \frac{8}{3}-1 = \frac{5}{3}\)…