$$ \begin{aligned} \frac{10}{20}+\frac{10}{x} &= 1&& \text{multiply ALL terms by } \color{blue}{ 20x }. \\[1 em]20x\cdot\frac{10}{20}+20x\cdot\frac{10}{x} &= 20x\cdot1&& \text{cancel out the denominators} \\[1 em]10x+200 &= 20x&& \text{move the $ \color{blue}{ 20x } $ to the left side and $ \color{blue}{ 200 }$ to the right} \\[1 em]10x-20x &= -200&& \text{simplify left side} \\[1 em]-10x &= -200&& \text{ divide both sides by $ -10 $ } \\[1 em]x &= \frac{-200}{-10}&& \\[1 em]x &= 20&& \\[1 em] \end{aligned} $$

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