Question
$$x-\frac{3}{x} = 6$$
Answer
$$ \begin{matrix}x_1 = 3-2 \sqrt{ 3 } & x_2 = 3+2 \sqrt{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x-\frac{3}{x} &= 6&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx-x\cdot\frac{3}{x} &= x\cdot6&& \text{cancel out the denominators} \\[1 em]x^2-3 &= 6x&& \text{move all terms to the left hand side } \\[1 em]x^2-3-6x &= 0&& \text{simplify left side} \\[1 em]x^2-6x-3 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-6x-3 = 0 $ is a quadratic equation.
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