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