$$\frac{1}{x+4}+\frac{2}{x-4} = 6$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 1 }{ 4 }-\dfrac{\sqrt{ 2409 }}{ 12 } & x_2 = \dfrac{ 1 }{ 4 }+\dfrac{\sqrt{ 2409 }}{ 12 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x+4}+\frac{2}{x-4} &= 6&& \text{multiply ALL terms by } \color{blue}{ (x+4)(x-4) }. \\[1 em](x+4)(x-4)\cdot\frac{1}{x+4}+(x+4)(x-4)\cdot\frac{2}{x-4} &= (x+4)(x-4)\cdot6&& \text{cancel out the denominators} \\[1 em]x-4+2x+8 &= 6x^2-96&& \text{simplify left side} \\[1 em]3x+4 &= 6x^2-96&& \text{move all terms to the left hand side } \\[1 em]3x+4-6x^2+96 &= 0&& \text{simplify left side} \\[1 em]-6x^2+3x+100 &= 0&& \\[1 em] \end{aligned} $$
$ -6x^{2}+3x+100 = 0 $ is a quadratic equation.
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