Question
$$\frac{x-2}{x+3} = \frac{3x}{2}$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = -\dfrac{ 4 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x-2}{x+3} &= \frac{3x}{2}&& \text{multiply ALL terms by } \color{blue}{ (x+3)\cdot2 }. \\[1 em](x+3)\cdot2 \cdot \frac{x-2}{x+3} &= (x+3)\cdot2 \cdot \frac{3x}{2}&& \text{cancel out the denominators} \\[1 em]2x-4 &= 3x^2+9x&& \text{move all terms to the left hand side } \\[1 em]2x-4-3x^2-9x &= 0&& \text{simplify left side} \\[1 em]-3x^2-7x-4 &= 0&& \\[1 em] \end{aligned} $$
$ -3x^{2}-7x-4 = 0 $ is a quadratic equation.
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