$$ \begin{aligned} \frac{1}{5}+\frac{1}{x} &= \frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 5x\cdot4 }. \\[1 em]5x\cdot4\cdot\frac{1}{5}+5x\cdot4\cdot\frac{1}{x} &= 5x\cdot4\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]4x+20 &= 5x&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ 20 }$ to the right} \\[1 em]4x-5x &= -20&& \text{simplify left side} \\[1 em]-x &= -20&& \text{switch signs on both sides} \\[1 em]x &= 20&& \\[1 em] \end{aligned} $$

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