$$ \begin{aligned} \frac{x}{x+1} &= \frac{5}{4}&& \text{multiply ALL terms by } \color{blue}{ (x+1)\cdot4 }. \\[1 em](x+1)\cdot4 \cdot \frac{x}{x+1} &= (x+1)\cdot4\cdot\frac{5}{4}&& \text{cancel out the denominators} \\[1 em]4x &= 5x+5&& \text{move the $ \color{blue}{ 5x } $ to the left side} \\[1 em]4x-5x &= 5&& \text{simplify left side} \\[1 em]-x &= 5&& \text{switch signs on both sides} \\[1 em]x &= -5&& \\[1 em] \end{aligned} $$

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