Factorize to remove the square root. How to factorize $$\pm \sqrt{x^{-6}-x^6-4}$$so that the square root can be removed?
Don't know where to start!

Unfortunately, unlike $-x^8+2-x^{-8}=-(x^4-x^{-4})^2=i^2(x^4-x^{-4})^2,$ the radicand $x^{-6}-x^6-4$ is not factorable as a perfect square, so the given expression is probably the best you're going to get. You could always rewrite it as $$\frac1{|x^3|}\sqrt{1-x^{12}-4x^6},$$ but that isn't really much of an improvement.
