Question
$$\frac{2}{3}x+\frac{1}{4}x = \frac{11}{x}$$
Answer
$$ \begin{matrix}x_1 = -2 \sqrt{ 3 } & x_2 = 2 \sqrt{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{3}x+\frac{1}{4}x &= \frac{11}{x}&& \text{multiply ALL terms by } \color{blue}{ 3\cdot4x }. \\[1 em]3\cdot4x \cdot \frac{2}{3}x+3\cdot4x\frac{1}{4}x &= 3\cdot4x\cdot\frac{11}{x}&& \text{cancel out the denominators} \\[1 em]8x^2+3x^2 &= 132&& \text{simplify left side} \\[1 em]11x^2 &= 132&& \text{move all terms to the left hand side } \\[1 em]11x^2-132 &= 0&& \\[1 em] \end{aligned} $$
$ 11x^{2}-132 = 0 $ is a quadratic equation.
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