$$\frac{1}{5}+\frac{1}{6} = \frac{1}{x}$$

$$ \begin{aligned} \frac{1}{5}+\frac{1}{6} &= \frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ 5\cdot6x }. \\[1 em]5\cdot6x\cdot\frac{1}{5}+5\cdot6x\cdot\frac{1}{6} &= 5\cdot6x\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]6x+5x &= 30&& \text{simplify left side} \\[1 em]11x &= 30&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{30}{11}&& \\[1 em] \end{aligned} $$

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