Question
$$(1-x)\frac{x+1}{12}+1 = 1+x$$
Answer
$$ \begin{matrix}x_1 = -6-\sqrt{ 37 } & x_2 = -6+\sqrt{ 37 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (1-x)\frac{x+1}{12}+1 &= 1+x&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12(1-x)\frac{x+1}{12}+12\cdot1 &= 12\cdot1+12x&& \text{cancel out the denominators} \\[1 em]-x^2+1+12 &= 12+12x&& \text{simplify left and right hand side} \\[1 em]-x^2+13 &= 12x+12&& \text{move all terms to the left hand side } \\[1 em]-x^2+13-12x-12 &= 0&& \text{simplify left side} \\[1 em]-x^2-12x+1 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-12x+1 = 0 $ is a quadratic equation.
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