$$ \begin{aligned} \frac{4}{x}+12 &= 14&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{4}{x}+x\cdot12 &= x\cdot14&& \text{cancel out the denominators} \\[1 em]4+12x &= 14x&& \text{move the $ \color{blue}{ 14x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]12x-14x &= -4&& \text{simplify left side} \\[1 em]-2x &= -4&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-4}{-2}&& \\[1 em]x &= 2&& \\[1 em] \end{aligned} $$

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