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TS EAMCET · Maths · Functions

If \(\frac{(x+1)}{(2 x-1)(3 x+1)}=\frac{A}{(2 x-1)}+\frac{B}{(3 x+1)}\), then \(16 A+9 B\) is equal to

  1. A \(4\)
  2. B \(5\)
  3. C \(6\)
  4. D \(8\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(6\)

Step-by-step Solution

Detailed explanation

Given that, \( \begin{aligned} & \frac{x+1}{(2 x-1)(3 x+1)}=\frac{A}{(2 x-1)}+\frac{B}{(3 x+1)} \\ \Rightarrow & (x+1)=A(3 x+1)+B(2 x-1) \\ \Rightarrow & (x+1)=x(3 A+2 B)+A-B \end{aligned} \) On equating the coefficient of \(x\) and constant on both sides, we get \(3 A+2 B=1\)…