$$\frac{1}{x}-3+\frac{2}{x}+2 = 0$$

$$ \begin{aligned} \frac{1}{x}-3+\frac{2}{x}+2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x}-x\cdot3+x\cdot\frac{2}{x}+x\cdot2 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]1-3x+2+2x &= 0&& \text{simplify left side} \\[1 em]-x+3 &= 0&& \text{ move the constants to the right } \\[1 em]-x &= -3&& \text{switch signs on both sides} \\[1 em]x &= 3&& \\[1 em] \end{aligned} $$

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