$$ \begin{aligned} \frac{3+x}{2-x} &= \frac{1}{2}&& \text{multiply ALL terms by } \color{blue}{ (2-x)\cdot2 }. \\[1 em](2-x)\cdot2 \cdot \frac{3+x}{2-x} &= (2-x)\cdot2\cdot\frac{1}{2}&& \text{cancel out the denominators} \\[1 em]2x+6 &= 2-x&& \text{move the $ \color{blue}{ -x } $ to the left side and $ \color{blue}{ 6 }$ to the right} \\[1 em]2x+x &= 2-6&& \text{simplify left and right hand side} \\[1 em]3x &= -4&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{4}{3}&& \\[1 em] \end{aligned} $$

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