Let
n=x+1+x2
The asking expression is simplified as
n(y+1+y2)=1
y+1+y2=n1
1+y2=n1−y
(1+y2)2=(n1−y)2
1+y2=n21−n2y+y2
n21−n2y=1
−2y=n−n1
y=21(n1−n) (1)
n1−n
=x+1+x21−(x+1+x2)
=(x+1+x2)(x−1+x2)x−1+x2−(x+1+x2)
=−1x−1+x2−(x+1+x2)
=−2x
∴y=−x
(x+y)2=0