Q51 / 160 · AP EAMCET 2007 · Mathematics

If $\frac{3 x}{(x-a)(x-b)}=\frac{2}{x-a}+\frac{1}{x-b}$, then $a: b$ is equal to

  • A
    $1: 2$
  • Correct answer
    B
    $-2: 1$
  • C
    $1: 3$
  • D
    $3: 1$

Solution

$\begin{aligned} & \text { Given, } \frac{3 x}{(x-a)(x-b)}=\frac{2}{(x-a)}+\frac{1}{(x-b)} \\ & \Rightarrow \quad 3 x=2(x-b)+1(x-a)\end{aligned}$ On comparing the coefficient of constant term, we get $\begin{aligned} & & -2 b-a & =0 \\ \Rightarrow & & \frac{a}{b} & =-\frac{2}{1} \\ \Rightarrow & & a: b & =-2: 1\end{aligned}$

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

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