$$\frac{2}{x}+\frac{x}{3} = x-1$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 3 }{ 4 }-\dfrac{\sqrt{ 57 }}{ 4 } & x_2 = \dfrac{ 3 }{ 4 }+\dfrac{\sqrt{ 57 }}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{x}+\frac{x}{3} &= x-1&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3\cdot\frac{2}{x}+x\cdot3\frac{x}{3} &= x\cdot3x-x\cdot3\cdot1&& \text{cancel out the denominators} \\[1 em]6+x^2 &= 3x^2-3x&& \text{simplify left side} \\[1 em]x^2+6 &= 3x^2-3x&& \text{move all terms to the left hand side } \\[1 em]x^2+6-3x^2+3x &= 0&& \text{simplify left side} \\[1 em]-2x^2+3x+6 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}+3x+6 = 0 $ is a quadratic equation.
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