$$3 \cdot \frac{x}{x+1} = \frac{12}{(x-1)(x+1)}+2$$

$$ \begin{aligned} 3 \cdot \frac{x}{x+1} &= \frac{12}{(x-1)(x+1)}+2&& \text{multiply ALL terms by } \color{blue}{ (x+1)(x-1) }. \\[1 em](x+1)(x-1)\cdot3 \cdot \frac{x}{x+1} &= (x+1)(x-1)\cdot\frac{12}{(x-1)(x+1)}+(x+1)(x-1)\cdot2&& \text{cancel out the denominators} \\[1 em]3x^2-3x &= 12x^2+24x+12+2x^2-2&& \text{simplify right side} \\[1 em]3x^2-3x &= 14x^2+24x+10&& \text{move all terms to the left hand side } \\[1 em]3x^2-3x-14x^2-24x-10 &= 0&& \text{simplify left side} \\[1 em]-11x^2-27x-10 &= 0&& \\[1 em] \end{aligned} $$

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