Find all real numbers such that $\sqrt{x-\frac{1}{x}} + \sqrt{1 - \frac{1}{x}} = x$ Find all real numbers such that 
$$\sqrt{x-\frac{1}{x}} + \sqrt{1 - \frac{1}{x}} = x$$
My attempt to the solution :
I tried to square both sides and tried to remove the root but the equation became of 6th degree.Is there an easier method to solve this?

Let's multiply
$$
\sqrt{x-1/x} + \sqrt{1 - 1/x} = x\tag{1}
$$
by $(\sqrt{x-1/x} - \sqrt{1 - 1/x})$. Then we get
$$
x-1=x(\sqrt{x-1/x} - \sqrt{1 - 1/x})
$$
$$
\sqrt{x-1/x} - \sqrt{1 - 1/x}=1-1/x\tag{2}
$$
Sum up $(1)$ and $(2)$ to get
$$
2\sqrt{x-1/x}=x-1/x+1
$$
Now make the substitution $y=\sqrt{x-1/x}$. The rest is clear.
