Explanation

(b)
Let $f(x) = \log_{e}\frac{x - 2}{x - 3}$
$f(x)$ is defined either $(x - 2) > 0,\ (x - 3) > 0$ or $(x - 2) < 0$
$(x - 3) < 0$ or $x \neq 2,\ 3$
$\Rightarrow f(x)$ is defined either $x > 3$ or $x < 2$ or $x \neq 2,\ 3$
$ie,\ x \in ( - \infty,\ 2) \cup (3,\ \infty)$