$$\frac{5}{x+2}+\frac{1}{2} = 3$$

$$ \begin{aligned} \frac{5}{x+2}+\frac{1}{2} &= 3&& \text{multiply ALL terms by } \color{blue}{ (x+2)\cdot2 }. \\[1 em](x+2)\cdot2\cdot\frac{5}{x+2}+(x+2)\cdot2\cdot\frac{1}{2} &= (x+2)\cdot2\cdot3&& \text{cancel out the denominators} \\[1 em]10+x+2 &= 6x+12&& \text{simplify left side} \\[1 em]x+12 &= 6x+12&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]x-6x &= 12-12&& \text{simplify left and right hand side} \\[1 em]-5x &= 0&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{0}{-5}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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