7. The solution set of the inequality $\frac{1}{x^{2}-2 x+2}+\lg \frac{1-x^{2}+2 x}{1+x^{2}-2 x}$ $<\frac{1}{2}$ is
7. $(1-\sqrt{2}, 0) \cup(2,1+\sqrt{2})$

Let $x^{2}-2 x=t$, then $\frac{1}{t+2}+\lg \frac{1-t}{1+t}<\frac{1}{2}$
Let $f(t)=\frac{1}{t+2}+\lg \frac{1-t}{1+t}$, we know $f(t)<f(0)$. The domain of $f(t)$ is $(-1,1)$, and it is monotonically decreasing on this interval. Therefore, the solution to (1) is $0<t<1$.
So $0<x^{2}-2 x<1$, the solution to this inequality is $1-\sqrt{2}<x<0$ or $2<x<1+\sqrt{2}$.