$$ \begin{aligned} 9 \cdot \frac{x}{5-x} &= 76&& \text{multiply ALL terms by } \color{blue}{ 5-x }. \\[1 em](5-x)\cdot9 \cdot \frac{x}{5-x} &= (5-x)\cdot76&& \text{cancel out the denominators} \\[1 em]9x &= -76x+380&& \text{move the $ \color{blue}{ -76x } $ to the left side} \\[1 em]9x+76x &= 380&& \text{simplify left side} \\[1 em]85x &= 380&& \text{ divide both sides by $ 85 $ } \\[1 em]x &= \frac{380}{85}&& \\[1 em]x &= \frac{76}{17}&& \\[1 em] \end{aligned} $$

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