Solution
= Solution
Rewrite the <rational function> as
$$
g(x)=\frac12\left(1-\frac1{x-1}\right).
$$
If $x>2$, then $x-1>1$, so $0<1/(x-1)<1$. Subtracting from $1$ and dividing by $2$ proves
$$
\boxed{0<g(x)<\frac12\quad(x>2)}.
$$
= Solution
Rewrite the <rational function> as
$$
g(x)=\frac12\left(1-\frac1{x-1}\right).
$$
If $x>2$, then $x-1>1$, so $0<1/(x-1)<1$. Subtracting from $1$ and dividing by $2$ proves
$$
\boxed{0<g(x)<\frac12\quad(x>2)}.
$$