### Instruction: What is the simplified value of $\frac{10! + 11! + 12!}{10! + 11!}$?### Response: I notice that both the numerator and the denominator have a factor of 10!, so I can divide both by that and simplify.
I get $\frac{10! + 11! + 12!}{10! + 11!} = \frac{1 + 11 + 11 \cdot 12}{1 + 11}$.
Now I can simplify further by expanding the brackets and combining like terms.