$\frac{x ^{2} + x + 1}{x - 1} = 0$

Answer

$x_{1} = - \frac{1}{2} + \frac{3}{2} i x_{2} = - \frac{1}{2} - \frac{3}{2} i$

Explanation

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

$x^{2} + x + 1 = 0$ 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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x−1x2+x+1​=0

x1​=−21​+23​​i​x2​=−21​−23​​i​

$\frac{x ^{2} + x + 1}{x - 1} = 0$

$x_{1} = - \frac{1}{2} + \frac{3}{2} i x_{2} = - \frac{1}{2} - \frac{3}{2} i$