(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve [tex]\frac{|x^2-5x+4|}{|x^2-4|}\le1[/tex]

2. Relevant equations

3. The attempt at a solution

as

[tex]|x^2-4|[/tex]will be positive always

cross multiply and take 1 to other side of equation

solve by taking LCM

we get

[tex]|x^2-5x+4|-(x^2-4)\le0[/tex]

on solving we get

[tex](x^2-5x+4)-(x^2-4)\le0[/tex] and [tex]-(x^2-5x+4)-(x^2-4)\le0[/tex]

the other method I know is to square to remove the modulus function

[tex](x^2-5x+4)^2-(x^2-4)^2\le0[/tex]

among these which method is correct?

the second method becomes equation of degree 4 i.e.[tex]x^4....[/tex]

please provide hints.

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# Homework Help: Solve for modulus inequality.

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