Hey, the given inequality is as follows:
(4-x2)2>(x2-4x+4)2
I begin with factoring both sides of the inequality as follows:
(-2+x)2(2+x)2>(x-2)4
Here is where I run into an issue. If I divide by (x-2)2 and get the following:
(2+x)2>(x-2)2 I lose a solution because solving this now gives me the solution of x>0.
If I instead divide the entire RHS (2+x)2/(x-2)2>1 It yields the correct solutions 0<x<2 II x > 2
What is it I am overlooking?
(4-x2)2>(x2-4x+4)2
I begin with factoring both sides of the inequality as follows:
(-2+x)2(2+x)2>(x-2)4
Here is where I run into an issue. If I divide by (x-2)2 and get the following:
(2+x)2>(x-2)2 I lose a solution because solving this now gives me the solution of x>0.
If I instead divide the entire RHS (2+x)2/(x-2)2>1 It yields the correct solutions 0<x<2 II x > 2
What is it I am overlooking?