$$2x = 3-\frac{1}{x}$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = \dfrac{ 1 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x &= 3-\frac{1}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2x &= x\cdot3-x\cdot\frac{1}{x}&& \text{cancel out the denominators} \\[1 em]2x^2 &= 3x-1&& \text{move all terms to the left hand side } \\[1 em]2x^2-3x+1 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-3x+1 = 0 $ is a quadratic equation.
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