Question
$$x\cdot3+\frac{1}{x}\cdot3 = 0$$
Answer
$$ \begin{matrix}x_1 = i & x_2 = -i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x\cdot3+\frac{1}{x}\cdot3 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx\cdot3+x \cdot \frac{1}{x}\cdot3 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]3x^2+3 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+3 = 0 $ is a quadratic equation.
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