Gosh! I thought I had it already!?

x^(u^2 - 3)/x^(u - 3)
= x^[(u^2 - 3) - (u - 3)]
= x^(u^2 - 3 - u + 3)
= x^(u^2 - u)

We call the "fraction bar thing" as a "vinculum".

x^{ u^2 - 3 }
-----------------
x^(u - 3)

= x^{ (u^2 - 3) - (u - 3) }

= x^{u^2 - 3 - u + 3}

= x^{u^2 - u)

= x^[ u(u - 1) ]

The horizontal line is called a solidus.

Upper part of a fraction is called numerator.

Bottom part of a fraction is called denominator.

x^[u^2-3]-u+3=x^(u^2-u)=x^u(u-1)

x^(u^2-3-u+3)=x^(u^2-u)

when you divide powers, you substract the exponents
x^a/x^b=x^(a-b)
so the result is

x^(u^2-u) as u^2-3 -(u-3)=u^2-u