$$(x+1+\frac{2x+2}{x-1})\frac{x}{x\cdot2+x} = 0$$
Answer
$$ x = -1 $$
Explanation
$$ \begin{aligned} (x+1+\frac{2x+2}{x-1})\frac{x}{x\cdot2+x} &= 0&& \text{simplify left side} \\[1 em](x+1+\frac{2x+2}{x-1})\frac{x}{3x} &= 0&& \\[1 em]\frac{x^2+2x+1}{x-1}\frac{x}{3x} &= 0&& \\[1 em]\frac{x^3+2x^2+x}{3x^2-3x} &= 0&& \\[1 em]\frac{x^2+2x+1}{3x-3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3x-3 }. \\[1 em](3x-3)\frac{x^2+2x+1}{3x-3} &= (3x-3)\cdot0&& \text{cancel out the denominators} \\[1 em]x^2+2x+1 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+2x+1 = 0 $ is a quadratic equation.
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