$$ \begin{aligned} \frac{1}{x+2} &= 3&& \text{multiply ALL terms by } \color{blue}{ x+2 }. \\[1 em](x+2)\cdot\frac{1}{x+2} &= (x+2)\cdot3&& \text{cancel out the denominators} \\[1 em]1 &= 3x+6&& \text{ swap the left and right side of the equation } \\[1 em]3x+6 &= 1&& \text{ move 6 to the right } \\[1 em]3x &= 1-6&& \\[1 em]3x &= -5&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{5}{3}&& \\[1 em] \end{aligned} $$

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