Question
$$\frac{12}{x+2}+\frac{2}{x-2} = 3$$
Answer
$$ \begin{matrix}x_1 = \dfrac{ 2 }{ 3 } & x_2 = 4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{12}{x+2}+\frac{2}{x-2} &= 3&& \text{multiply ALL terms by } \color{blue}{ (x+2)(x-2) }. \\[1 em](x+2)(x-2)\cdot\frac{12}{x+2}+(x+2)(x-2)\cdot\frac{2}{x-2} &= (x+2)(x-2)\cdot3&& \text{cancel out the denominators} \\[1 em]12x-24+2x+4 &= 3x^2-12&& \text{simplify left side} \\[1 em]14x-20 &= 3x^2-12&& \text{move all terms to the left hand side } \\[1 em]14x-20-3x^2+12 &= 0&& \text{simplify left side} \\[1 em]-3x^2+14x-8 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+14x-8 = 0 $ is a quadratic equation.
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