$$\frac{1}{x} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{1}{x} &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x} &= x\cdot0&& \text{cancel out the denominators} \\[1 em]1 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 1 = 0 } $ is FALSE, we conclude that the equation has no solution.
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