$$ \begin{aligned} \frac{1}{x}+1+\frac{1}{x}+2 &= \frac{2}{x}+10&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x}+x\cdot1+x\cdot\frac{1}{x}+x\cdot2 &= x\cdot\frac{2}{x}+x\cdot10&& \text{cancel out the denominators} \\[1 em]1+x+1+2x &= 2+10x&& \text{simplify left and right hand side} \\[1 em]3x+2 &= 10x+2&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 2 }$ to the right} \\[1 em]3x-10x &= 2-2&& \text{simplify left and right hand side} \\[1 em]-7x &= 0&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= \frac{0}{-7}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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