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

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

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