$$\frac{1}{x^2} = \frac{2}{x^2+x-2}$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 7 }}{ 2 }i & x_2 = \dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 7 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x^2} &= \frac{2}{x^2+x-2}&& \text{multiply ALL terms by } \color{blue}{ x^2(x^2+x-2) }. \\[1 em]x^2(x^2+x-2)\cdot\frac{1}{x^2} &= x^2(x^2+x-2)\cdot\frac{2}{x^2+x-2}&& \text{cancel out the denominators} \\[1 em]x^2+x-2 &= 2x^2&& \text{move all terms to the left hand side } \\[1 em]x^2+x-2-2x^2 &= 0&& \text{simplify left side} \\[1 em]-x^2+x-2 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+x-2 = 0 $ is a quadratic equation.
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