$$\frac{3}{k}-\frac{1}{2} = \frac{12}{k}$$

$$ \begin{aligned} \frac{3}{k}-\frac{1}{2} &= \frac{12}{k}&& \text{multiply ALL terms by } \color{blue}{ k\cdot2 }. \\[1 em]k\cdot2\cdot\frac{3}{k}-k\cdot2\cdot\frac{1}{2} &= k\cdot2\cdot\frac{12}{k}&& \text{cancel out the denominators} \\[1 em]6-k &= 24&& \text{ move 6 to the right } \\[1 em]-k &= 24-6&& \\[1 em]-k &= 18&& \text{switch signs on both sides} \\[1 em]k &= -18&& \\[1 em] \end{aligned} $$

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