11.55 Simplify the fraction $\frac{n!}{(n+1)!-n!}$.
11.55 Using the definition of factorial, we find

$$
\frac{n!}{(n+1)!-n!}=\frac{1 \cdot 2 \cdot 3 \cdot \ldots \cdot n}{n!(n+1-1)}=\frac{1 \cdot 2 \cdot 3 \cdot \ldots \cdot n}{n!n}=\frac{n!}{n!n}=\frac{1}{n}
$$

Answer: $\frac{1}{n}$.