Expressions with (6/x+2) + (8/x+3)

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Discussion Overview

The discussion revolves around how to combine the expressions (6/x+2) + (8/x+3), focusing on the mathematical process of finding a common denominator for addition of fractions. The scope includes mathematical reasoning and clarification of operations involving fractions.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant, Val, questions how to combine the expressions and mentions inverting and multiplying, suggesting some confusion about the operations involved.
  • Another participant provides a method for combining the fractions by finding a common denominator, specifically stating it as (x+2)(x+3).
  • A later reply clarifies that inverting and multiplying is applicable for division by a fraction, not for addition.
  • One participant illustrates the process of finding a common denominator by comparing it to a simpler example of adding fractions with different denominators.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial confusion regarding the operations, but there is agreement on the method of finding a common denominator for the addition of the fractions.

Contextual Notes

There is some ambiguity in Val's understanding of the operations involved, particularly regarding when to invert and multiply, which is not fully resolved in the discussion.

Who May Find This Useful

This discussion may be useful for individuals seeking clarification on adding fractions, particularly those who are confused about the operations involved in manipulating algebraic expressions.

ValiantKhan
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If i have something like (6/x+2) + (8/x+3) how to i do that?

aren't i supposed to invert and multiply or something, thanks

--Val
 
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[tex]\frac{6(x+3)}{(x+2)(x+3)} + \frac{8(x+2)}{(x+2)(x+3)}[/tex]

You just need to find a common denominator.
 
ValiantKhan said:
aren't i supposed to invert and multiply or something, thanks

That's for division by a fraction, in which case you multiply by the reciprocal.
 
Since the two denominators are x+2 and x+3 the common denominator will be (x+2)(x+3).

It's just like 1/2+ 1/3= (1/2)(3/3)+ (1/3)(2/2)= 3/6+ 2/6= 5/6.
 

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