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

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

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