jmc

We do a little factoring, taking advantage of the properties of factorials: $$\frac{10!+11!+12!}{10!+11!}=\frac{10!(1+11+11\cdot 12)}{10!(1+11)}=\frac{1+11+11\cdot 12}{12}=\frac{12+11\cdot 12}{12}=\frac{12\cdot 12}{12}=\boxed{12}.$$