Finding the composition f°f when f(x)=x/(x+1)

[najatau]

Homework Statement

Find f°f

Homework Equations

f(x)=x/x+1

The Attempt at a Solution

$$\frac{x}{x+1}$$ divided by $$\frac{x}{x+1}$$ I got $$\frac{1}{x+1}+1$$ but I know the answer in the book is $$\frac{x}{2x+1}$$. I'm not sure how the book arrived at that answer.

 

[mfb]

How did you get your result?

 

[vela]

Homework Statement

Find f°f

Homework Equations

f(x)=x/x+1

You mean f(x) = x/(x+1), right? Because what you wrote simplifies to f(x)=2 for x≠0.

The Attempt at a Solution

$$\frac{x}{X+1}divided by\frac{x}{x+1}$$

Are X and x supposed to be the same variable? If not, what's X? If they're supposed to be the same, use the same letter.

How did you come up with that division? Please explain what you're doing in more detail.

I got $$\frac{1}{x+1}+1$$ but I know the answer in the book is $$\frac{x}{2x+1}$$. I'm not sure how the book arrived at that answer.

 

[najatau]

Thanks for responding. I just found out why I got the wrong answer. I wasn't dividing complex/compound fractions with monomials in the denominator correctly. I tried to multiply the numerator by the reciprocal of the denominator instead of finding the lowest common denominator for the numerator and denominator like I saw in this video.

I got the book's answer when I did it the way the video instructed. Not sure why I didn't get the same answer either way.
(:-/