If $y=\frac{{\sin }^{4}x-{\cos }^{4}x+{\sin }^{2}x{\cos }^{2}x}{{\sin }^{4}x+{\cos }^{4}x+{\sin }^{2}x{\cos }^{2}x},x\in (0,\frac{\pi }{2})$ , then

We have 

$y=\frac{{\sin }^{4}x-{\cos }^{4}x+{\sin }^{2}x{\cos }^{2}x}{{\sin }^{4}x+{\cos }^{4}x+{\sin }^{2}x{\cos }^{2}x},x\in (0,\frac{\pi }{2})$

$$\begin{gathered} y=\frac{{\tan }^{4}x+{\tan }^{2}x-1}{{\tan }^{4}x+{\tan }^{2}x+1}=1-\frac{2}{{\tan }^{4}x+{\tan }^{2}x+1} \\ \Rightarrow \boxed{-1\le y<1} \end{gathered}$$