$$ \begin{aligned} \frac{3}{x}-2-5\frac{x}{x}+1 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{3}{x}-x\cdot2-x\cdot5\frac{x}{x}+x\cdot1 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]3-2x-5x+x &= 0&& \text{simplify left side} \\[1 em]-6x+3 &= 0&& \text{ move the constants to the right } \\[1 em]-6x &= -3&& \text{ divide both sides by $ -6 $ } \\[1 em]x &= \frac{-3}{-6}&& \\[1 em]x &= \frac{1}{2}&& \\[1 em] \end{aligned} $$

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