$$\frac{1}{1+2e} = 1$$

$$ \begin{aligned} \frac{1}{1+2e} &= 1&& \text{multiply ALL terms by } \color{blue}{ 1+2e }. \\[1 em](1+2e)\cdot\frac{1}{1+2e} &= (1+2e)\cdot1&& \text{cancel out the denominators} \\[1 em]1 &= 2e+1&& \text{ swap the left and right side of the equation } \\[1 em]2e+1 &= 1&& \text{ move 1 to the right } \\[1 em]2e &= 1-1&& \\[1 em]2e &= 0&& \text{ divide both sides by $ 2 $ } \\[1 em]e &= \frac{0}{2}&& \\[1 em]e &= 0&& \\[1 em] \end{aligned} $$

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