Question
$$\frac{1}{x^2}-16 = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 4 } & x_2 = -\dfrac{ 1 }{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x^2}-16 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot\frac{1}{x^2}-x^2\cdot16 &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]1-16x^2 &= 0&& \text{simplify left side} \\[1 em]-16x^2+1 &= 0&& \\[1 em] \end{aligned} $$
$ -16x^{2}+1 = 0 $ is a quadratic equation.
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