Need help to simplify irrational equation

Question

I have faced a problem simplifying this equation. . I tried to solve it this way: , but I just can't get the correct answer. This equation is from high school course, so it must have quite a simple solution, so maybe you will be able to help me :)

Answer 1

Square both sides of $\sqrt{y} + \sqrt{\frac{1}{y}} = 1$ to get $y + 2 + \frac{1}{y} = 1$; this is the quadratic $y^2 + y + 1 = 0$ with roots $y = \frac{2x+1}{x-1} = \frac{-1\pm\sqrt{-5}}{2}$. So there are no real values of $x$ for which the equation holds.