Question
$$(x+1)\frac{3x+2}{x-1} = 0$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = -\dfrac{ 2 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x+1)\frac{3x+2}{x-1} &= 0&& \text{simplify left side} \\[1 em]\frac{3x^2+5x+2}{x-1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-1 }. \\[1 em](x-1)\frac{3x^2+5x+2}{x-1} &= (x-1)\cdot0&& \text{cancel out the denominators} \\[1 em]3x^2+5x+2 &= 0&& \\[1 em] \end{aligned} $$
$ 3x^{2}+5x+2 = 0 $ is a quadratic equation.
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