simplify

\(\dfrac{10!+11!+12!}{10!+11!}\\~\\ \ =\ \dfrac{10!\ +\ 11\cdot10!\ +\ 12\cdot11\cdot10!}{10!\ +\ 11\cdot10!}\\~\\ \ =\ \dfrac{10!(\ 1\ +\ 11\ +\ 12\cdot11\ )}{10!(\ 1\ +\ 11\ )}\\~\\ \ =\ \dfrac{1\ +\ 11\ +\ 12\cdot11}{1\ +\ 11}\\~\\ \ =\ \dfrac{1\ +\ 11\ +\ 132}{1\ +\ 11}\\~\\ \ =\ \dfrac{144}{12}\\~\\ \ =\ 12\)

 

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