Why does the denominator at 0:38 have to be "x + 1"?

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[Originally posted in Discussions]
Why does the denominator at 6:24 have to be "x + 1"?

Hey there, thanks for asking such a good question! Let's take a look...
We can start with what "x" is. Here is how it is defined.
Now let's try and figure out what "x+1" is, by adding 1 to both sides.
Wait a second, this looks a little familiar... where have we seen this before?
Yes! It's just the denominator of the fraction! (remember the dots just mean the pattern keeps going)
So since what is in the blue box and "x+1" are the same thing, we can replace one with the other.
There you go! The denominator is just "x+1".
I hope that answers your question. If you have any other questions or clarifications, just shoot us another email.
Best,
"The Daily Challenge Team