$$\frac{x+5}{x+7} = \frac{9}{5}$$

$$ \begin{aligned} \frac{x+5}{x+7} &= \frac{9}{5}&& \text{multiply ALL terms by } \color{blue}{ (x+7)\cdot5 }. \\[1 em](x+7)\cdot5 \cdot \frac{x+5}{x+7} &= (x+7)\cdot5\cdot\frac{9}{5}&& \text{cancel out the denominators} \\[1 em]5x+25 &= 9x+63&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 25 }$ to the right} \\[1 em]5x-9x &= 63-25&& \text{simplify left and right hand side} \\[1 em]-4x &= 38&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{38}{4}&& \\[1 em]x &= -\frac{19}{2}&& \\[1 em] \end{aligned} $$

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