Solving an Inequation with Fractions: 1° Equation Help

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Homework Help Overview

The discussion revolves around solving an inequality involving fractions, specifically the expression \(\frac{1}{x-1} + \frac{2}{x-2} - \frac{3}{x-3} < 0\). The original poster expresses frustration in simplifying the problem, indicating that their attempts have led to a higher degree equation instead of the expected first-degree equation.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss methods for combining fractions and simplifying the expression. Some suggest re-evaluating the steps taken to combine the fractions, while others question the correctness of the algebraic manipulations performed by the original poster.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts. There is a focus on identifying errors in the algebraic process and encouraging the original poster to show intermediate steps for better guidance. No consensus has been reached on a solution, but several participants are actively engaging in clarifying misunderstandings.

Contextual Notes

Participants note the importance of mastering elementary algebra skills, emphasizing that the forum's rules prevent providing complete solutions. The original poster expresses a desire for more direct assistance, reflecting a struggle with the material and the pressure of upcoming exams.

  • #31


I got to the solution! :eek::eek::smile:

\frac{1}{x-1}+\frac{2}{x-2}-\frac{3}{x-3}<0

\frac{1(x-2)(x-3)+2(x-1)(x-3)-3(x-1)(x-2)}{(x-1)(x-2)(x-3)}

(x-2)(x-3)=x²-3x-2x+6

(2x-2(x-3)=2x²-6x-2x+6=2x²-8x+6

-3x+3(x-2)=-3x²+6x+3x+6=-3x²+9x-6\frac{-4x+6}{(x-1)(x-2)(x-3)}

-4x+6<0 --> -4x<-6 --> x>3/2

x-1>0 --> x>1

x-2>0 --> x>2

x-3>0 --> x>3

S={x E R/x<1 or 3/2<x<2 or x>3}

So guys,I thank you all very much to show that i could do this by myself!

Now I believe "Yes we can".
 
Last edited:
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