$\text{a)}$  

Zał:

$a^2{b}^2\ne 0,a-b\ne 0,a+b\ne 0$  

$a\ne 0,b\ne 0,a\ne b,a\ne -b$  

 

$\frac{a^2+ab}{a^2{b}^2}\left(\frac{a}{a-b}-\frac{a}{a+b}\right)=\frac{a^2+ab}{a^2{b}^2}\left(\frac{a\left(a+b\right)}{\left(a-b\right)\left(a+b\right)}-\frac{a\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}\right)=$  

$=\frac{a^2+ab}{a^2{b}^2}\left(\frac{a^2+ab-a^2+ab}{\left(a-b\right)\left(a+b\right)}\right)=\frac{\sout{a\left(a+b\right)}}{\sout{a^2}\cdot b^{\sout{2}}}\cdot \frac{2\cdot \sout{ab}}{\left(a-b\right)\cdot \sout{\left(a+b\right)}}=\frac{2}{b\left(a-b\right)}$  

---

$\text{b)}$  

Zał:

$a-1\ne 0,a^2\ne 0,b\ne 0,b-ab\ne 0$  

$a\ne 1,a\ne 0,b\ne 0,b\left(1-a\right)\ne 0$  

$a\ne 1,a\ne 0,b\ne 0$  

 

${\left(a-\frac{a^2}{a-1}\right)}^{-1}\left(\frac{a+1}{b}-\frac{1}{b-ab}\right)={\left(\frac{a\left(a-1\right)}{a-1}-\frac{a^2}{a-1}\right)}^{-1}\left(\frac{a+1}{b}-\frac{1}{b\left(1-a\right)}\right)=$  

$={\left(\frac{a^2-a-a^2}{a-1}\right)}^{-1}\left(\frac{\left(a+1\right)\left(1-a\right)}{b\left(1-a\right)}-\frac{1}{b\left(1-a\right)}\right)={\left(\frac{-a}{a-1}\right)}^{-1}\left(\frac{a-a^2+1-a-1}{b\left(1-a\right)}\right)=$   

$=\frac{a-1}{\sout{-a}}\cdot \frac{\sout{-a}\cdot a}{b\left(1-a\right)}=\frac{\sout{\left(a-1\right)}\cdot a}{-b\cdot \sout{\left(a-1\right)}}=-\frac{a}{b}$