6. $\left|-\frac{3}{x-1}\right|>\left|-\frac{x-2}{2}\right|$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

6. $\left|-\frac{3}{x-1}\right|>\left|-\frac{x-2}{2}\right|$.
6. This inequality can be rewritten as: $\frac{3}{|1-x|}>\frac{|2-x|}{2}$.

From this, $|1-x| \cdot|2-x|0 \\ x^{2}-3 x-40$, since $D<0$, the inequality holds for any $x$;

b) $x^{2}-3 x-4<0,-1<x<4$. Answer: $-1<x<4$.