$$\frac{4}{x}+\frac{1}{3x} = 9$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 27 }{ 2 }-\dfrac{\sqrt{ 681 }}{ 2 } & x_2 = \dfrac{ 27 }{ 2 }+\dfrac{\sqrt{ 681 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{4}{x}+\frac{1}{3x} &= 9&& \text{multiply ALL terms by } \color{blue}{ x\cdot3 }. \\[1 em]x\cdot3\cdot\frac{4}{x}+x\cdot3\cdot\frac{1}{3x} &= x\cdot3\cdot9&& \text{cancel out the denominators} \\[1 em]12+x^2 &= 27x&& \text{simplify left side} \\[1 em]x^2+12 &= 27x&& \text{move all terms to the left hand side } \\[1 em]x^2+12-27x &= 0&& \text{simplify left side} \\[1 em]x^2-27x+12 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-27x+12 = 0 $ is a quadratic equation.
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