$$\frac{9}{x+1} = \frac{2}{x^2-1}$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = \dfrac{ 11 }{ 9 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{9}{x+1} &= \frac{2}{x^2-1}&& \text{multiply ALL terms by } \color{blue}{ (x+1)(x^2-1) }. \\[1 em](x+1)(x^2-1)\cdot\frac{9}{x+1} &= (x+1)(x^2-1)\cdot\frac{2}{x^2-1}&& \text{cancel out the denominators} \\[1 em]9x^2-9 &= 2x+2&& \text{move all terms to the left hand side } \\[1 em]9x^2-9-2x-2 &= 0&& \text{simplify left side} \\[1 em]9x^2-2x-11 &= 0&& \\[1 em] \end{aligned} $$
$ 9x^{2}-2x-11 = 0 $ is a quadratic equation.
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