Answer
This equation has no real solutions.
Work Step by Step
$\dfrac{1}{x-1}-\dfrac{2}{x^{2}}=0$
Evaluate the substraction:
$\dfrac{x^{2}-2(x-1)}{x^{2}(x-1)}=0$
Take $x^{2}(x-1)$ to multiply the right side. We are left with:
$x^{2}-2x+2=0$
Solve using the quadratic formula. Here, $a=1$, $b=-2$ and $c=2$:
$x=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(2)}}{2(1)}=\dfrac{2\pm\sqrt{4-8}}{2}=\dfrac{2\pm\sqrt{-4}}{2}$
$x=\dfrac{2\pm2i}{2}=1\pm i$
