\[(b - 2)x = b^{2} - 4\]
\[x = \frac{b^{2} - 4}{b - 2}\]
\[x = \frac{(b - 2)(b + 2)}{b - 2},\ \ \ \ b \neq 2\]
\[x = b + 2\]
\[b + 2 > 0\]
\[b > - 2\]
\[Ответ:b \in ( - 2;2) \cup (2;\ + \infty).\]