Solve $\displaystyle \frac{|x^2-5x+4|}{|x^2-4|}\le1$

as

$\displaystyle |x^2-4|$will be positive always

cross multiply and take 1 to other side of equation

solve by taking LCM

we get

|x^2-5x+4|-(x^2-4)\le0

on solving we get

$\displaystyle (x^2-5x+4)-(x^2-4)\le0$ and $\displaystyle -(x^2-5x+4)-(x^2-4)\le0$

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

$\displaystyle (x^2-5x+4)^2-(x^2-4)^2\le0$

among these which method is correct?

the second method becomes equation of degree 4 i.e.$\displaystyle x^4$)

please provide hints.