Question
$$x+\frac{3}{x}-\frac{x}{x}-2 = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 3 }}{ 2 }i & x_2 = \dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 3 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+\frac{3}{x}-\frac{x}{x}-2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx+x\cdot\frac{3}{x}-x\frac{x}{x}-x\cdot2 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]x^2+3-x-2x &= 0&& \text{simplify left side} \\[1 em]x^2-3x+3 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-3x+3 = 0 $ is a quadratic equation.
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