Question
$$\frac{x}{x}-2 = x+\frac{2}{x}+1$$
Answer
$$ \begin{matrix}x_1 = -1+i & x_2 = -1-i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x}{x}-2 &= x+\frac{2}{x}+1&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x \cdot \frac{x}{x}-x\cdot2 &= xx+x\cdot\frac{2}{x}+x\cdot1&& \text{cancel out the denominators} \\[1 em]x-2x &= x^2+2+x&& \text{simplify left and right hand side} \\[1 em]-x &= x^2+x+2&& \text{move all terms to the left hand side } \\[1 em]-x-x^2-x-2 &= 0&& \text{simplify left side} \\[1 em]-x^2-2x-2 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-2x-2 = 0 $ is a quadratic equation.
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