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Question
\[\frac{x}{x - 5} > \frac{1}{2}\]
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Solution
\[\frac{x}{x - 5} > \frac{1}{2}\]
\[ \Rightarrow \frac{x}{x - 5} - \frac{1}{2} > 0\]
\[ \Rightarrow \frac{2x - x + 5}{2(x - 5)} > 0\]
\[ \Rightarrow \frac{x + 5}{2(x - 5)} > 0\]
\[ \Rightarrow \frac{x + 5}{x - 5} > 0\]
\[\therefore x \in \left( - \infty , - 5 \right) \cup \left( 5, \infty \right)\]
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