Question
$$x-\frac{\frac{3}{3}}{x}-3 = 0$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 13 }}{ 2 } & x_2 = \dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 13 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x-\frac{\frac{3}{3}}{x}-3 &= 0&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3x-x\cdot3 \cdot \frac{\frac{3}{3}}{x}-x\cdot3\cdot3 &= x\cdot3\cdot0&& \text{cancel out the denominators} \\[1 em]3x^2-3-9x &= 0&& \text{simplify left side} \\[1 em]3x^2-9x-3 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}-9x-3 = 0 $ is a quadratic equation.
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