y = ( 1 - x ) ( 1 + x ^ { 2 } ) ^ { - 1 } x = 0

Answer 1

getting rid of the extraneous braces, I see
(1-x)x / (1+x^2) = 0
since the denominator is never zero, just worry about the numerator.
x(1-x) = 0
x=0 or x=1