17 Given that $a+\frac{1}{a+1}=b+\frac{1}{b-1}-2$ and $a-b+2 \neq 0$, find the value of $a b-a+b$.
17 Answer: (2)
Let $x=a+1, y=b-1(x-y \neq 0)$, then $x-1+\frac{1}{x}=y+1+\frac{1}{y}-2 \Rightarrow x+\frac{1}{x}=y+\frac{1}{y}$ $\Rightarrow(x-y)\left(1-\frac{1}{x y}\right)=0 \Rightarrow x y=1 \Rightarrow a b-a+b=2$.