Solve for x (complex solution)
x\in \frac{\sqrt{1-iy^{-\frac{1}{4}}}}{2},-\frac{\sqrt{1-iy^{-\frac{1}{4}}}}{2},-\frac{\sqrt{1-y^{-\frac{1}{4}}}}{2},\frac{\sqrt{1-y^{-\frac{1}{4}}}}{2},-\frac{\sqrt{y^{-\frac{1}{4}}+1}}{2},\frac{\sqrt{y^{-\frac{1}{4}}+1}}{2},-\frac{\sqrt{iy^{-\frac{1}{4}}+1}}{2},\frac{\sqrt{iy^{-\frac{1}{4}}+1}}{2}
y\neq 0
Solve for y (complex solution)
y=\frac{1}{\left(4x^{2}-1\right)^{4}}
x\neq -\frac{1}{2}\text{ and }x\neq \frac{1}{2}
Solve for x
\left\{\begin{matrix}x=-\frac{\sqrt{\sqrt[4]{y}-1}}{2\sqrt[8]{y}}\text{; }x=\frac{\sqrt{\sqrt[4]{y}-1}}{2\sqrt[8]{y}}\text{, }&y\geq 1\\x=-\frac{\sqrt{\sqrt[4]{y}+1}}{2\sqrt[8]{y}}\text{; }x=\frac{\sqrt{\sqrt[4]{y}+1}}{2\sqrt[8]{y}}\text{, }&y>0\end{matrix}\right.
Solve for y
y=\frac{1}{\left(4x^{2}-1\right)^{4}}
|x|\neq \frac{1}{2}
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