$$\frac{1}{3}-\frac{1}{x} = \frac{5}{6}$$

$$ \begin{aligned} \frac{1}{3}-\frac{1}{x} &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ 3x\cdot6 }. \\[1 em]3x\cdot6\cdot\frac{1}{3}-3x\cdot6\cdot\frac{1}{x} &= 3x\cdot6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]6x-18 &= 15x&& \text{move the $ \color{blue}{ 15x } $ to the left side and $ \color{blue}{ -18 }$ to the right} \\[1 em]6x-15x &= 18&& \text{simplify left side} \\[1 em]-9x &= 18&& \text{ divide both sides by $ -9 $ } \\[1 em]x &= -\frac{18}{9}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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