Explanation

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