Question
$$\frac{1}{x}+\frac{1}{x+2} = \frac{3}{4}$$
Answer
$$ \begin{matrix}x_1 = 2 & x_2 = -\dfrac{ 4 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}+\frac{1}{x+2} &= \frac{3}{4}&& \text{multiply ALL terms by } \color{blue}{ x(x+2)\cdot4 }. \\[1 em]x(x+2)\cdot4\cdot\frac{1}{x}+x(x+2)\cdot4\cdot\frac{1}{x+2} &= x(x+2)\cdot4\cdot\frac{3}{4}&& \text{cancel out the denominators} \\[1 em]4x+8+4x &= 3x^2+6x&& \text{simplify left side} \\[1 em]8x+8 &= 3x^2+6x&& \text{move all terms to the left hand side } \\[1 em]8x+8-3x^2-6x &= 0&& \text{simplify left side} \\[1 em]-3x^2+2x+8 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}+2x+8 = 0 $ is a quadratic equation.
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