# Homework Help: Need help doing simple re-arrangement

1. Jun 13, 2010

1. The problem statement, all variables and given/known data

How do you go from:

(2x)/(2x+1)

and rearrange to get:

1-[(1)/(2x+1)]?

My book goes directly from 1 to the other before doing the integration and both are the same, but can someone explain how this rearrangement is done?

Thanks!

2. Jun 13, 2010

### Staff: Mentor

You can (almost) always replace 1 by (anything)/(anything). In this case they used 1 = (2x+1)/(2x+1).

3. Jun 13, 2010

### njama

They used little trick:
$$\frac{2x}{2x+1}=\frac{(2x+1)-1}{2x+1}=1-\frac{1}{2x+1}$$

4. Jun 13, 2010

Sorry haha but im still confused as to what you did exactly.

5. Jun 13, 2010

### VeeEight

The first step is that 2x = (2x + 1) - 1

$$\frac{(2x+1)-1}{2x+1}= \frac{2x+1}{2x+1} - \frac{1}{2x+1} = 1-\frac{1}{2x+1}$$

since $$\frac{2x+1}{2x+1} = 1$$

6. Jun 13, 2010