$\frac{x}{x + 1} = \frac{1}{x}$

Answer

$x_{1} = \frac{1}{2} - \frac{5}{2} x_{2} = \frac{1}{2} + \frac{5}{2}$

Explanation

\frac{x}{x + 1} (x + 1) x \cdot \frac{x}{x + 1} x^{2} x^{2} - x - 1 = \frac{1}{x} = (x + 1) x \cdot \frac{1}{x} = x + 1 = 0 multiply ALL terms by (x + 1) x . cancel out the denominators move all terms to the left hand side

$x^{2} - x - 1 = 0$ is a quadratic equation.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.

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$\frac{x}{x + 1} = \frac{1}{x}$

$x_{1} = \frac{1}{2} - \frac{5}{2} x_{2} = \frac{1}{2} + \frac{5}{2}$