$$\frac{1}{6}+\frac{1}{3} = \frac{1}{x}$$

$$ \begin{aligned} \frac{1}{6}+\frac{1}{3} &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ 6\cdot3x }. \\[1 em]6\cdot3x\cdot\frac{1}{6}+6\cdot3x\cdot\frac{1}{3} &= 6\cdot3x\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]3x+6x &= 18&& \text{simplify left side} \\[1 em]9x &= 18&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{18}{9}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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