Question
$$6 \cdot \frac{x}{x^2-2} = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} 6 \cdot \frac{x}{x^2-2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2-2 }. \\[1 em](x^2-2)\cdot6 \cdot \frac{x}{x^2-2} &= (x^2-2)\cdot0&& \text{cancel out the denominators} \\[1 em]6x &= 0&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{0}{6}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$
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