Divide each term by 4x:
[tex]\sf\dfrac{96x^3+36x^2+4x-1}{4x}[/tex]
[tex]\sf\dfrac{96x^3}{4x}+\dfrac{36x^2}{4x}+\dfrac{4x}{4x}-\dfrac{1}{4x}[/tex]
Just divide them separately.
96/4 = 24
x^3/x = x^2
So our first term is 24x^2.
36/4 = 9
x^2/x = x
So our second term is 9x.
4x/4x = 1
Anything divided by itself is 1. This is our 3rd term.
-1/4x, we can't simplify this any further, so this is our last term.
So we have:
[tex]\boxed{\sf 24x^2+9x+1-\dfrac{1}{4x}}[/tex]