$$ \begin{aligned} 8 \cdot \frac{x}{x}+1 &= 2&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot8 \cdot \frac{x}{x}+x\cdot1 &= x\cdot2&& \text{cancel out the denominators} \\[1 em]8x+x &= 2x&& \text{simplify left side} \\[1 em]9x &= 2x&& \text{move the $ \color{blue}{ 2x } $ to the left side} \\[1 em]9x-2x &= 0&& \text{simplify left side} \\[1 em]7x &= 0&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= \frac{0}{7}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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