$$\frac{1}{x}-1(x+1) = 4$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 5 }{ 2 }-\dfrac{\sqrt{ 29 }}{ 2 } & x_2 = -\dfrac{ 5 }{ 2 }+\dfrac{\sqrt{ 29 }}{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}-1(x+1) &= 4&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{1}{x}-x\cdot1(x+1) &= x\cdot4&& \text{cancel out the denominators} \\[1 em]1-(x^2+x) &= 4x&& \text{simplify left side} \\[1 em]1-x^2-x &= 4x&& \\[1 em]-x^2-x+1 &= 4x&& \text{move all terms to the left hand side } \\[1 em]-x^2-x+1-4x &= 0&& \text{simplify left side} \\[1 em]-x^2-5x+1 &= 0&& \\[1 em] \end{aligned} $$
$ -x^{2}-5x+1 = 0 $ is a quadratic equation.
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