$$x+\frac{1}{x} = 0$$
Answer
$$ \begin{matrix}x_1 = i & x_2 = -i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+\frac{1}{x} &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx+x\cdot\frac{1}{x} &= x\cdot0&& \text{cancel out the denominators} \\[1 em]x^2+1 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+1 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
This page was created using
Equations Solver