Tricky inequality

Hope is in the Domain, I think.

Immediately, we have:

x > 0
x <= 5

A little less obvious is:

x ≠ 4

That is a very, very messy algebra problem. A quick graph makes a couple of things suspicious, mainly that the expression EQUALS 2 right around x = 1 and x = 5/2. It turns out that these are exact solutions. THAT was lucky!

Knowing that, we just have to test each region, as defined by the Domain and the two points of equality.

For 0 < x < 1, the expression is greater than 2.
For 1 < x < 5/2, the expression is less than 2.
For 5/2 < x < 4, the expression is greater than 2.
For 4 < x <= 5, the expression is less than 2.

If we hadn't simply stumbled over the two solutions for equality, we might STILL be working the algebra.

So, are we getting anywhere or do you REALLY want to wade through the algebra?
 
Grandioso!!. The first thing I did (out of habbit), was defining the domain so xЄ]0;5]; x≠4 is there. I thought about analyzing the function the "right way" i.e. taking a derivative and looking at extreme points, but decided that I am missing something. Here is a trick I came up with just now. If we split 2 on the right side as 1+1, take 1 to the left and negative fraction to the right and do the addition, we will end up with two fractions with identical numerators.
Anyways, thanks a million!
 
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