How to Simplify a Fraction to Quadratic Form?

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Discussion Overview

The discussion revolves around the process of simplifying the fraction \(\frac{12x+9}{x}\) to achieve a quadratic form represented by the equation \(x^2 - 3x - 9 = 0\). Participants explore various steps and methods to arrive at this form, focusing on algebraic manipulation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant requests assistance in simplifying the fraction to a quadratic form, indicating confusion about the steps involved.
  • Another participant points out a potential error in the original equation, suggesting that the right-hand side should be \(9x\) instead of \(9\).
  • A different participant provides a step-by-step explanation, detailing how to multiply both sides by \(x\), cancel the denominator, and expand the right-hand side to derive the quadratic equation.
  • Subsequent responses acknowledge the provided solution and express gratitude for the clarification.
  • One participant expresses confusion about how to arrive at the quadratic form, indicating a misunderstanding of the earlier steps.

Areas of Agreement / Disagreement

There is some disagreement regarding the initial setup of the equation, with differing views on the correct form of the right-hand side. However, the steps to simplify the fraction to the quadratic form appear to be generally accepted by participants who engage with the solution provided.

Contextual Notes

Some assumptions about the manipulation of algebraic expressions may be implicit, and there is a lack of clarity regarding the initial conditions set by the original problem. The discussion does not resolve all potential misunderstandings related to the algebraic steps.

alpha01
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can someone show how to simplify [tex]\frac{12x+9}{x} = x+9[/tex] so that it is in the quadratic form: x^2 -3x -9 = 0

multiplying both sides by x, subtracting both sides by 9 etc. . doesn't give me the quadratic.
 
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Hi alpha01! :smile:

erm … I think you put 9 on the right-hand side instead of 9x. :redface:
 
Just multiply both sides by 'x' :

( x (12x + 9 ) ) / x = x ( x + 9 )

multiplied x on the left hand side cancels out with its denominator & by expanding the right hand side you will get;

12x + 9 = x^2 + 9x

Subtracting both sides by (12x + 9);

0 = x^2 +9x - 12x - 9

which means;

x^2 - 3x - 9 = 0

& that's what you are looking for...
 
mubashirmansoor said:
Subtracting both sides by (12x + 9);
thanks
 
Your welcome ! :)
 
tiny-tim said:
Hi alpha01! :smile:

erm … I think you put 9 on the right-hand side instead of 9x. :redface:

how would he get a quadratic then :confused:
 
sorry misread and now i can't delete
 

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