Question 4
Determine the greatest value of
$$\frac2{x^2+1}-\frac2{y^2+1}+\frac3{z^2+1}$$
for positive real numbers $x,y,z$ satisfying $xyz+x+z=y$.
$$\frac2{x^2+1}-\frac2{y^2+1}+\frac3{z^2+1}$$
for positive real numbers $x,y,z$ satisfying $xyz+x+z=y$.