$$\frac{1}{3}+\frac{2}{x} = \frac{1}{5}$$

$$ \begin{aligned} \frac{1}{3}+\frac{2}{x} &= \frac{1}{5}&& \text{multiply ALL terms by } \color{blue}{ 3x\cdot5 }. \\[1 em]3x\cdot5\cdot\frac{1}{3}+3x\cdot5\cdot\frac{2}{x} &= 3x\cdot5\cdot\frac{1}{5}&& \text{cancel out the denominators} \\[1 em]5x+30 &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 30 }$ to the right} \\[1 em]5x-3x &= -30&& \text{simplify left side} \\[1 em]2x &= -30&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= -\frac{30}{2}&& \\[1 em]x &= -15&& \\[1 em] \end{aligned} $$

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