AMO · 2027 · Grades 8-9 · Self-study SET 20 Question 9

Define $n!=n\times(n-1)\times\cdots\times2\times1$. For example, $4!=4\times3\times2\times1=24$ and $3!=3\times2\times1=6$. Simplify
$$\frac{41!+40!}{3\times39!+2\times39!+39!}.$$
Choose one option.