Question

Alguém me ajuda com essa questão?$\frac{x}{1-x} + \frac{x-2}{x}-1$=0 Existe duas raízes para resolvê-la.

Answer 1

$\frac{x}{1-x} + \frac{x-2}{x} -1=0\\ \\ \frac{\not{x^2}+3x-\not{x}^2-2-x+x^2}{x(1-x)} =0\\ \\x^2+2x-2=0\\ \\\Delta=4-4*1*(-2)\\\Delta=12\\ \\x= \frac{-b\pm\sqrt{\Delta}}{2a}\\ \\x= \frac{-2\pm \sqrt{12} }{2} \\ \\x= \frac{-2\pm 2\sqrt{3} }{2}$

$x= \frac{\not2(-1\pm \sqrt{3} )}{\not2} \\ \\\boxed{\boxed{\therefore~x=-1\pm \sqrt{3} }}$