begin{array}{l} nx + frac{1}{x} - 1 = frac{3}{4} nx + frac{1}{x} = frac{7}{4} n(4x^2 + 4 - 7x) /4x = 0 nx neq 0 n4x^2 - 7x + 4 = 0 nD = 49 - 4 cdot 4 cdot 4 = -15 n end{array} Answer: x = frac{1}{8} (7 pm i cdot sqrt{15}) - 2 complex solutions

Answer in Geometry for jonathan kim #22968

Question #22968

X+1/x-1=3/4

Expert's answer

\begin{array}{l} x + \frac{1}{x} - 1 = \frac{3}{4} \\ x + \frac{1}{x} = \frac{7}{4} \\ (4x^2 + 4 - 7x)/4x = 0 \\ x \neq 0 \\ 4x^2 - 7x + 4 = 0 \\ D = 49 - 4 \cdot 4 \cdot 4 = -15 \\ \end{array}

Answer: $x = \frac{1}{8} (7 \pm i \cdot \sqrt{15}) - 2$ complex solutions

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