7. The function
$$
y=\frac{1}{\sqrt{x^{2}-6 x+8}}+\log _{2}\left(\frac{x+3}{x-1}-2\right)
$$

has the domain $\qquad$
$$
\text { II. 7. }(1,2) \cup(4,5) \text {. }
$$

From the problem, we know
$$
\left\{\begin{array}{l}
x^{2}-6 x+8>0, \\
\frac{x+3}{x-1}-2>0
\end{array} \Rightarrow x \in(1,2) \cup(4,5)\right. \text {. }
$$