$$ \begin{aligned} 10 &= \frac{x}{x+5}&& \text{multiply ALL terms by } \color{blue}{ x+5 }. \\[1 em](x+5)\cdot10 &= (x+5)\frac{x}{x+5}&& \text{cancel out the denominators} \\[1 em]10x+50 &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 50 }$ to the right} \\[1 em]10x-x &= -50&& \text{simplify left side} \\[1 em]9x &= -50&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= -\frac{50}{9}&& \\[1 em] \end{aligned} $$

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