Need help doing simple re-arrangement

  • Thread starter adelaide87
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In summary, the conversation discusses how to rearrange the expression (2x)/(2x+1) to get 1-[(1)/(2x+1)], which is used in integration. The person asking the question is confused about the steps involved and the expert explains that it involves replacing 1 with (2x+1)/(2x+1) and using a little trick to rewrite the expression. The expert also clarifies this by using the example of (3x)/(4x+1). Overall, the key concept is to replace 1 with (anything)/(anything) and use algebraic manipulation to rearrange the expression.
  • #1
adelaide87
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0

Homework Statement



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!
 
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  • #2
You can (almost) always replace 1 by (anything)/(anything). In this case they used 1 = (2x+1)/(2x+1).
 
  • #3
They used little trick:
[tex]\frac{2x}{2x+1}=\frac{(2x+1)-1}{2x+1}=1-\frac{1}{2x+1}[/tex]
:smile:
 
  • #4
Sorry haha but I am still confused as to what you did exactly.
 
  • #5
The first step is that 2x = (2x + 1) - 1

[tex]
\frac{(2x+1)-1}{2x+1}= \frac{2x+1}{2x+1} - \frac{1}{2x+1} = 1-\frac{1}{2x+1}
[/tex]since [tex]
\frac{2x+1}{2x+1} = 1
[/tex]
 
  • #6
so what about this one:(3x)/(4x+1)

I don't understand if you are just bringing the bottom up, or how 2x = (2x + 1) - 1
 
  • #7
Okay nevermind, I see what you are doing. Didnt make sense at first, thank you for the help.
 

What is re-arrangement?

Re-arrangement is the process of changing the order or position of elements in a given set or sequence. In scientific terms, it refers to rearranging molecules or atoms to form new compounds or structures.

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Re-arrangement plays a crucial role in scientific research and experimentation. It allows scientists to better understand the properties and behavior of different substances and to create new compounds with specific characteristics.

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Some common methods for re-arrangement in science include chemical reactions, physical processes such as heating or cooling, and genetic engineering techniques. These methods can be used to rearrange molecules, atoms, or genetic material to achieve desired results.

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While re-arrangement can lead to important scientific discoveries and advancements, it can also pose potential risks. For example, re-arranging genetic material can have unintended consequences and could lead to the development of harmful organisms.

How can I get help with re-arrangement in my scientific work?

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