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

$$ \begin{aligned} \frac{3}{x}+2-\frac{1}{x} &= \frac{1}{5}&& \text{multiply ALL terms by } \color{blue}{ x\cdot5 }. \\[1 em]x\cdot5\cdot\frac{3}{x}+x\cdot5\cdot2-x\cdot5\cdot\frac{1}{x} &= x\cdot5\cdot\frac{1}{5}&& \text{cancel out the denominators} \\[1 em]15+10x-5 &= x&& \text{simplify left side} \\[1 em]10x+10 &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 10 }$ to the right} \\[1 em]10x-x &= -10&& \text{simplify left side} \\[1 em]9x &= -10&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= -\frac{10}{9}&& \\[1 em] \end{aligned} $$

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