<s>[INST] Rearranging the formula Transpose this formula to make $y$ the subject.
$$x=\sqrt{x^2y^2+1-y}$$
My try:
$$x^2=x^2y^2+1-y$$
$$x^2-x^2y^2=1-y$$
$$x^2(1-y^2)=1-y$$
Here I got 2 $y$ terms, but I am not sure what to do next.
 [/INST] If you can't see the factorization, treat the thing as a quadratic in $y$:
$$
x^2y^2-y+(1-x^2)=0
$$
The discriminant is
$$
1-4x^2(1-x^2)=4x^4-4x^2+1=(2x^2-1)^2
$$
Apply the quadratic formula:
$$
y=\frac{1\pm(2x^2-1)}{2x^2}
$$
and you find either $y=1$ or
$$
y=\frac{1-2x^2+1}{2x^2}=\frac{1-x^2}{x^2}
$$
</s>