Question
$$\frac{1}{x}+\frac{3}{x+2} = 2$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}+\frac{3}{x+2} &= 2&& \text{multiply ALL terms by } \color{blue}{ x(x+2) }. \\[1 em]x(x+2)\cdot\frac{1}{x}+x(x+2)\cdot\frac{3}{x+2} &= x(x+2)\cdot2&& \text{cancel out the denominators} \\[1 em]x+2+3x &= 2x^2+4x&& \text{simplify left side} \\[1 em]4x+2 &= 2x^2+4x&& \text{move all terms to the left hand side } \\[1 em]4x+2-2x^2-4x &= 0&& \text{simplify left side} \\[1 em]4x+2-2x^2-4x &= 0&& \\[1 em]-2x^2+2 &= 0&& \\[1 em] \end{aligned} $$
$ -2x^{2}+2 = 0 $ is a quadratic equation.
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