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