$$ \begin{aligned} \frac{3}{x}-\frac{1}{6} &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot6 }. \\[1 em]x\cdot6\cdot\frac{3}{x}-x\cdot6\cdot\frac{1}{6} &= x\cdot6\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]18-x &= 6&& \text{ move 18 to the right } \\[1 em]-x &= 6-18&& \\[1 em]-x &= -12&& \text{switch signs on both sides} \\[1 em]x &= 12&& \\[1 em] \end{aligned} $$

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