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.

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Now let's try and figure out what "x+1" is, by adding 1 to both sides.

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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)

61be5a5c-713c-46ff-94ad-953ab67c5f5c-image.png

So since what is in the blue box and "x+1" are the same thing, we can replace one with the other.

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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

That's a good question. You do need to do the little fraction inside the big fraction first. This gets into the meaning of what a fraction or a divide is (and it answers your other question, posted under "Also.").

One way to think of fractions (or divides) is as switched-around multiplication problems. So in \(\frac{2}{3},\) the "2" means something altogether that you are sharing, and "3" means the number of groups you are sharing them into. For example,

$$\frac{2 \text{ cookies}}{3 \text{ people}} $$.

The answer to this fraction means how much cookie each person gets. As a multiplication problem, this would be:

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And you could represent it as a picture of groups, like this:

3e261b13-fc3b-4fe0-9b1b-c0171daa04de-image.png

What if you divide by a fraction, like

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Compare this with

b462be17-db96-4474-8d79-c727d658be8e-image.png

There are half as many people, so each person should get more. How much more? They should get twice as much. This is why

c793a44c-da5f-4bfb-b6d1-dfe2f6cb9690-image.png

This works no matter if the numerator (top number) of the fraction is 1 or any other number.

This also explains why we have to do the little fraction first; we have to know how many people we are sharing the cookies with before we can begin to figure out how many cookies each person gets.

I hope this helps! Let me know if you have any more questions.

Happy Learning!

The Daily Challenge Team