$$\frac{1}{x}+1+\frac{2}{x^2}-1 = 1$$

$$ \begin{aligned} \frac{1}{x}+1+\frac{2}{x^2}-1 &= 1&& \text{multiply ALL terms by } \color{blue}{ xx^2 }. \\[1 em]xx^2\cdot\frac{1}{x}+xx^2\cdot1+xx^2\cdot\frac{2}{x^2}-xx^2\cdot1 &= xx^2\cdot1&& \text{cancel out the denominators} \\[1 em]1+x^3+\frac{2}{x^1}-x^3 &= x^3&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot1+x^1\cdot1x^3+x^1\cdot\frac{2}{x^1}-x^1\cdot1x^3 &= x^1\cdot1x^3&& \text{cancel out the denominators} \\[1 em]x+x^4+2-x^4 &= x^4&& \text{simplify left side} \\[1 em]x+x^4+2-x^4 &= x^4&& \\[1 em]x+2 &= x^4&& \text{move all terms to the left hand side } \\[1 em]x+2-x^4 &= 0&& \text{simplify left side} \\[1 em]-x^4+x+2 &= 0&& \\[1 em] \end{aligned} $$

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