$$ \begin{aligned} \frac{1}{x}+2 &= 3&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x}+x\cdot2 &= x\cdot3&& \text{cancel out the denominators} \\[1 em]1+2x &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]2x-3x &= -1&& \text{simplify left side} \\[1 em]-x &= -1&& \text{switch signs on both sides} \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$

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