Question
$$2 \cdot \frac{x}{x^2} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 2 \cdot \frac{x}{x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot2 \cdot \frac{x}{x^2} &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]\frac{2}{x^1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot\frac{2}{x^1} &= x^1\cdot0&& \text{cancel out the denominators} \\[1 em]2 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 2 = 0 } $ is FALSE, we conclude that the equation has no solution.
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