\(a\left(b-1\right)+2\left(b-1\right)=1\)
\(\Leftrightarrow\left(b-1\right)\left(a+2\right)=1\)
\(\Leftrightarrow a+2=\dfrac{1}{b-1}\) (b khác 1)
\(\Leftrightarrow a=\dfrac{1}{b-1}-2=\dfrac{-2b+3}{b-1}\)
vậy \(\left\{{}\begin{matrix}a=\dfrac{-2b+3}{b-1}\\b\in R\\b\ne1\end{matrix}\right.\)