$$ \begin{aligned} \frac{8}{13} &= 20-\frac{8}{x}&& \text{multiply ALL terms by } \color{blue}{ 13x }. \\[1 em]13x\cdot\frac{8}{13} &= 13x\cdot20-13x\cdot\frac{8}{x}&& \text{cancel out the denominators} \\[1 em]8x &= 260x-104&& \text{move the $ \color{blue}{ 260x } $ to the left side} \\[1 em]8x-260x &= -104&& \text{simplify left side} \\[1 em]-252x &= -104&& \text{ divide both sides by $ -252 $ } \\[1 em]x &= \frac{-104}{-252}&& \\[1 em]x &= \frac{26}{63}&& \\[1 em] \end{aligned} $$

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