$$ \begin{aligned} \frac{x}{x}-1+\frac{1}{x}+1+2\frac{x}{1}-x\cdot2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x\cdot1 }. \\[1 em]x\cdot1 \cdot \frac{x}{x}-x\cdot1\cdot1+x\cdot1\cdot\frac{1}{x}+x\cdot1\cdot1+x\cdot1\cdot2\frac{x}{1}-x\cdot1x\cdot2 &= x\cdot1\cdot0&& \text{cancel out the denominators} \\[1 em]x-x+1+x+2x^2-2x^2 &= 0&& \text{simplify left side} \\[1 em]x-x+1+x+2x^2-2x^2 &= 0&& \\[1 em]x+1 &= 0&& \text{ move the constants to the right } \\[1 em]x &= -1&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$

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