A：$f\left(x\right)=x-\frac{\ln \left|x\right|}{x^2}$

B：$f\left(x\right)=x+\frac{\ln \left|x\right|}{x^2}$

C：$f\left(x\right)=x^2-\frac{\ln \left|x\right|}{x}$

D：$f\left(x\right)=x+\frac{\ln \left|x\right|}{x}$