$$ \begin{aligned} \frac{6}{10} &= \frac{3}{x}+3&& \text{multiply ALL terms by } \color{blue}{ 10x }. \\[1 em]10x\cdot\frac{6}{10} &= 10x\cdot\frac{3}{x}+10x\cdot3&& \text{cancel out the denominators} \\[1 em]6x &= 30+30x&& \text{move the $ \color{blue}{ 30x } $ to the left side} \\[1 em]6x-30x &= 30&& \text{simplify left side} \\[1 em]-24x &= 30&& \text{ divide both sides by $ -24 $ } \\[1 em]x &= -\frac{30}{24}&& \\[1 em]x &= -\frac{5}{4}&& \\[1 em] \end{aligned} $$

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