The values of $x$ that satisfy $\frac{1}{x-1}>1$ are given by:
(a) $x<1$;
(c) $1<x<2$.

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

The values of $x$ that satisfy $\frac{1}{x-1}>1$ are given by:
(a) $x<1$;
(c) $1<x<2$.
The correct option is (c).

Note that the inverse of a number is only greater than 1 when the number is positive and less than 1. Therefore,

$$
\frac{1}{x-1}>1 \Longleftrightarrow 0<x-1<1 \Longleftrightarrow 1<x<2
$$