Simplify Fractions: (3-x)(x+2)(2x+9) < 0 | Multiply and Solve

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Homework Help Overview

The discussion revolves around simplifying a fraction inequality involving the expression (2x + 9) over the product of (3 - x) and (x + 2). Participants are exploring the transformation of the inequality into a product form.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the reasoning behind multiplying both sides of the inequality by (3 - x)²(x + 2)², questioning the implications of this transformation on the inequality's validity.

Discussion Status

There is an ongoing exploration of the steps involved in manipulating the inequality. Some participants provide insights into the positivity of the squared terms, while others are clarifying the rationale behind the multiplication step.

Contextual Notes

Participants are considering the effects of multiplying by expressions that may change the sign of the inequality, indicating a need for careful examination of assumptions regarding the values of x.

MrNeWBiE
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question in fractions,,,

how

2x+9/(3-x)(x+2) < 0

became



(3-x)(x+2)(2x+9) < 0 " multiply both sides "

zero is in the other side ,,,
 
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Hi MrNeWBiE! :smile:

'cos one is (3-x)2(x+2)2 times the other … which is always positive! :wink:
 


so i multiply both sides with ====> (3-x)^2(x+2)^2
 
(try using the X2 tag just above the Reply box :wink:)

Yup! :biggrin:
 

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