question_answer

What is function f satisfying the identity, \[f(x)+f\left( \frac{x-1}{x} \right)=1+x,\forall x\in -\,\{0.1\}\]?

A)  \[\frac{{{x}^{3}}-{{x}^{2}}-1}{x\,(x-1)}\]

B)  \[\frac{{{x}^{3}}-x+1}{x\,(x+1)}\]

C)  \[\frac{{{x}^{2}}-{{x}^{3}}+1}{x\,(x-1)}\]   

D)  \[\frac{{{x}^{3}}-{{x}^{2}}+1}{x\,(x-1)}\]