$$ \begin{aligned} \frac{1}{12} &= x+3&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot\frac{1}{12} &= 12x+12\cdot3&& \text{cancel out the denominators} \\[1 em]1 &= 12x+36&& \text{ swap the left and right side of the equation } \\[1 em]12x+36 &= 1&& \text{ move 36 to the right } \\[1 em]12x &= 1-36&& \\[1 em]12x &= -35&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= -\frac{35}{12}&& \\[1 em] \end{aligned} $$

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