a)

Aby wyznaczyć przedziały monotoniczności policzmy pierwszą pochodną funkcji.

$f{}^{\prime }\left(x\right)=\left(x^2\right){}^{\prime }-\left(2x\right){}^{\prime }+\left(\frac{x+1}{x-1}\right){}^{\prime }$  

$f{}^{\prime }\left(x\right)=2x-2+\frac{\left(x+1\right){}^{\prime }\cdot \left(x-1\right)-\left(x+1\right)\cdot \left(x-1\right){}^{\prime }}{{\left(x-1\right)}^2}$  

$f{}^{\prime }\left(x\right)=2x-2+\frac{1\cdot \left(x-1\right)-\left(x+1\right)\cdot 1}{{\left(x-1\right)}^2}$  

$f{}^{\prime }\left(x\right)=2x-2+\frac{x-1-x-1}{{\left(x-1\right)}^2}$  

$f{}^{\prime }\left(x\right)=2x-2+\frac{-2}{{\left(x-1\right)}^2}$