$$\frac{12+x}{x+8} = 1$$

$$ \begin{aligned} \frac{12+x}{x+8} &= 1&& \text{multiply ALL terms by } \color{blue}{ x+8 }. \\[1 em](x+8)\frac{12+x}{x+8} &= (x+8)\cdot1&& \text{cancel out the denominators} \\[1 em]12+x &= x+8&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]x-x &= 8-12&& \text{simplify left and right hand side} \\[1 em]x-x &= -4&& \\[1 em]0 &= -4&& \\[1 em] \end{aligned} $$

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