Question
$$\frac{6}{x}-3 = x-\frac{4}{x}$$
Answer
$$ \begin{matrix}x_1 = 2 & x_2 = -5 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{6}{x}-3 &= x-\frac{4}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{6}{x}-x\cdot3 &= xx-x\cdot\frac{4}{x}&& \text{cancel out the denominators} \\[1 em]6-3x &= x^2-4&& \text{move all terms to the left hand side } \\[1 em]6-3x-x^2+4 &= 0&& \text{simplify left side} \\[1 em]-x^2-3x+10 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-3x+10 = 0 $ is a quadratic equation.
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