Question

solve the quadratic equation : x÷(x-1)+(x-1)÷x=5÷2​

Answer 1

$\frac{x}{x - 1} + \frac{x - 1}{x} = \frac{5}{2} \\ \\ \frac{ {x}^{2} + {x}^{2} + 1 - x }{x(x - 1)} = \frac{5}{2} \\ \\ \frac{ {2x}^{2} - x + 1 }{ {x}^{2} - x } = \frac{5}{2} \\ \\ {4x}^{2} - 2x + 2 = {5x}^{2} - 5 \\ {4x}^{2} - {5x}^{2} - 2x +2 + 5 = 0 \\ { - x}^{2} - 2x + 7 = 0 \\ - x(x + 2) = - 7$

$.°. \: \: \: \: x = 7 \: \: \: or \: \: 5$