$
x ( (x^3 + 3x^2)^{1/3} + (x^2 + 2x - 3)^{1/2} )
$

So, I start off with breaking an x out from both parts of the equations and get:

$
x^2 \cdot ( (1 + 3/x)^{1/3} - (1 + 2/x - 3/x^{1/2} )^{1/2} )
$

Here comes the funky part - I try making two variable changes at the same time, refering to a standard maclaurin polynomial and get:
$
x^2 \cdot ( (1 + u)^{1/3} - (1 + t)^{1/2} ) =
x^2 \cdot ( 1 + u/3 - 1 + t/2 ) =
x^2 \cdot ( 1/x - 1/x + 3/2x^2 ) =
3/2
$

The answer should be 1, so, I assume I'm doing something wrong when I switch variables, any hint on what's going wrong?

2. I have no idea what you are doing! Are you taking the limit as x goes to something in particular? If so to what?

3. Oh lord, sorry, I missed adding that: X goes to infinity