<s>[INST] Simplification of surds $\frac{x}{\sqrt{x^2 - x^4}}$ 
$$\frac{x}{\sqrt{x^2 - x^4}}$$

I believe that I can factor out the $x^2$ in the square root to get
$$\frac{1}{\sqrt{1-x^2}} .$$
However, Wolfram Alpha doesn't do the simplification, hence my confusion.
 [/INST] $$\frac{x}{\sqrt{x^2 - x^4}}=
\Bigg\{\begin{array}{c}
       \frac{1}{\sqrt{1-x^2}}, \ \  0<x<1 \\
       -\frac{1}{\sqrt{1-x^2}}, \ \ -1<x<0
       \end{array}                 
$$
</s>