AP 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
- A \(4\)
- B \(5\)
- C \(6\)
- D \(8\)
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 On solving Eqs.…
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