Solve: $\sqrt{x-\frac1x}-\sqrt{1-\frac1x}=1-\frac1x$ for $ x\neq0$ $$\sqrt{x-\frac{1}{x}}-\sqrt{1-\frac{1}{x}}{=1-\frac{1}{x}}, x\neq0$$
So my idea is that I moved the second sqrt to the RHS and left the first on the LHS. I then squared everything and ended up with $\frac{x^2-1}{x}=2-\frac{3}{x}+\frac{1}{x^2}$. I don't know what to do next? Can somebody give a hint?

squaring two times and foctorizing we get
$$-\frac{(x-1)^2 \left(x^2-x-1\right)^2}{x^4}=0$$
if we do so 
we get
$$x-\frac{1}{x}=(1-\frac{1}{x})^2+1-\frac{1}{x}+2(1-\frac{1}{x})\sqrt{1-\frac{1}{x}}$$
the square root is missing !!
and you must square again!!!!!!!
