With some transformation in the first term

Algebra Level 3

Assume x, y, z are not negative, with condition: \[x^2+y^2+z^2=2\] Find maximum of the expression: \[\frac{x^2}{x^2+yz+x+1}+\frac{y+z}{x+y+z+1}-\frac{1+yz}{9}\]

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