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So the problem is:
ReplyDelete2023! / (2022! + 2021!)
If you remember your factorials, then you know you can rewrite the numerator as
2023•2022•2021!
In the denominator, you can rewrite 2022! as
2022•2021!
So now, you have a fraction that looks like this:
(2023•2022•2021!) / [(2022•2021!) + 2021!]
In the denominator, you can factor out the 2021!, so now your fraction looks like this:
(2023•2022•2021!) / 2021!(2022 + 1)
The (2022 + 1) obviously becomes 2023, so you now have this fraction:
(2023•2022•2021!) / 2021!(2023)
As you can see, the 2023s and 2021!s cancel each other out, so all you have left is
2022.
QED.