How do I simplify fractions with exponents?

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Homework Help Overview

The discussion revolves around simplifying fractions that involve exponents, specifically the expression (2x+3x)/6x and its equivalence to 2-x+3-x. Participants are exploring the manipulation of these expressions to achieve simplification.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss splitting the fraction into separate components and consider the implications of flipping bases and changing exponents. There is also an attempt to clarify the steps involved in the simplification process.

Discussion Status

The conversation is ongoing, with some participants providing guidance on how to approach the problem by suggesting the splitting of the fraction. However, there is no explicit consensus on the best method to simplify the expression, and various interpretations are being explored.

Contextual Notes

Some participants express uncertainty about the simplification process, indicating that they find the problem straightforward yet challenging to execute. There may be assumptions about the familiarity with exponent rules that are being questioned.

Aerospace93
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Homework Statement


(2x+3x)/6x = 2-x+3-x

I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!
 
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Aerospace93 said:

Homework Statement


(2x+3x)/6x = 2-x+3-x

I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!

Start by "splitting" the left side into two fractions, like this:
\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}
 
i certainly did that
 
(1/2)^x+(1/3)^x... which is the same as flipping them over and making the exponential -x. cool
 

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