Question:
$\frac{x}{x-5}>\frac{1}{2}$
Solution:
$\frac{x}{x-5}>\frac{1}{2}$
$\Rightarrow \frac{x}{x-5}-\frac{1}{2}>0$
$\Rightarrow \frac{2 x-x+5}{2(x-5)}>0$
$\Rightarrow \frac{x+5}{2(x-5)}>0$
$\Rightarrow \frac{x+5}{x-5}>0$
$\therefore x \in(-\infty,-5) \cup(5, \infty)$
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