$$\frac{2x+2}{x-1} = x+1$$
Answer
$$ \begin{matrix}x_1 = -1 & x_2 = 3 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2x+2}{x-1} &= x+1&& \text{multiply ALL terms by } \color{blue}{ x-1 }. \\[1 em](x-1)\frac{2x+2}{x-1} &= (x-1)x+(x-1)\cdot1&& \text{cancel out the denominators} \\[1 em]2x+2 &= x^2-x+x-1&& \text{simplify right side} \\[1 em]2x+2 &= x^2-1&& \text{move all terms to the left hand side } \\[1 em]2x+2-x^2+1 &= 0&& \text{simplify left side} \\[1 em]-x^2+2x+3 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+2x+3 = 0 $ is a quadratic equation.
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