Q132 / 200 · Manipal (MET) 2011 · Mathematics

If $\frac{e^x+2}{\left(e^x-1\right)\left(2 e^x-3\right)}=-\frac{3}{e^x-1}+\frac{B}{2 e^x-3}$, then $B$ is equal to

  • A
    1
  • B
    3
  • C
    5
  • Correct answer
    D
    7

Solution

Here, $e^x+2=-3\left(2 e^x-3\right)+B\left(e^x-1\right)$ On equating the coefficient of $e^x$ and constant, we get $\begin{aligned} & 1=-6+B \\ & 2=9-B \Rightarrow B=7\end{aligned}$

Hence, the correct answer is option: 'D'.

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