`a)` ĐKXĐ : \(\left\{ \begin{array}{l}x-1\ne0\\1+x\ne0\\x^2-1\ne0\end{array} \right.\) `⇒` \(\left\{ \begin{array}{l}x\ne1\\x\ne-1\\|x|\ne1\end{array} \right.\) `⇒ x \ne \pm1`
`b)` `B = (1/(x-1)-1/(1+x)+1)\div 1/(x^2-1)`
`= ((1+x-(x-1))/((x-1)(1+x))+1) * (x^2-1)`
`= ((1+x-x+1)/((x-1)(1+x)) + 1)*(x-1)(x+1)`
`= (2/((x-1)(1+x)) + 1) * (x-1)(x+1)`
`= (2+(x-1)(1+x))/((x-1)(1+x)) * (x-1)(x+1)`
`= 2 + (x-1)(x+1)`
`= 2 + x^2 - 1`
`= 1 + x^2`