Question

how do i simplify (1-(x/(1+x)))/(1+(x/(1+x)))

Answer 1

It's going to be sorta difficult, but the trick is to multiply by a clever form of the number 1, since multiplying by one doesn't change anything. Here's how it works, and you can use it anywhere:

This is my own made up example, so I used n instead of x so I don't confuse you.
\[\frac{1}{1+\frac{1}{n}} =\frac{1}{(1+\frac{1}{n})} \frac{n}{n} = \frac{n}{n+1} \]

It's sorta tricky so you might have to think about it for a bit and if you're stuck I can help you out.

Answer 2

yes i understand the concept:D i'm just having trouble with this specific example the double division is throwing me off D:

Answer 3

try something out, the worst that could happen is that you accidentally get it right. Then I can see how to help you out, like what part's confusing.

Answer 4

okay one second ill try and type it all out

Answer 5

if you want it might be easier to draw it out

Answer 6

okay well i have like a page of trial and error ill just tell you what im doing wrong other wise itll take me forever D:

Answer 7

okay so i isolated the numerator and the denominator and gave the numerator a common denominator of (1+(x/1+x))

Answer 8

wait no thats stupid im multiplying i dont need a common denominator .... ugh half a bloody page of useless work

Answer 9

Hey well that's a good catch though! You probably won't make that mistake again on a test where it actually counts at least.

Answer 10

Just to be sure before I give you a hint, is this the question:

\[\Large \frac{1-\frac{x}{1+x}}{1+\frac{x}{1+x}}\]

I just want to make sure that's what you're looking at cause there's a lot of stuff in there that can mess up haha.

Answer 11

complex fractions.

Answer 12

you know what it'd be rather hectic explaining this through text or using that retched drawing tool, i think iv got it from here.

Go help Some one else ill just use a calculator or something:)

Answer 13

Well alright haha I'll give you a hint anyways. Multiply by this form of 1 and distribute it out:

\[\frac{1+x}{1+x}\]

good luck

Answer 14

thanks !