Question
$$6 = \frac{x^2+x}{x-1}$$
Answer
$$ \begin{matrix}x_1 = 2 & x_2 = 3 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 6 &= \frac{x^2+x}{x-1}&& \text{multiply ALL terms by } \color{blue}{ x-1 }. \\[1 em](x-1)\cdot6 &= (x-1)\frac{x^2+x}{x-1}&& \text{cancel out the denominators} \\[1 em]6x-6 &= x^2+x&& \text{move all terms to the left hand side } \\[1 em]6x-6-x^2-x &= 0&& \text{simplify left side} \\[1 em]-x^2+5x-6 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}+5x-6 = 0 $ is a quadratic equation.
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