Divide 4w to every term separately.
[tex]\sf\dfrac{48w^3+128w^2+4w-1}{4w}[/tex]
[tex]\sf\dfrac{48w^3}{4w}+\dfrac{128w^2}{4w}+\dfrac{4w}{4w}-\dfrac{1}{4w}[/tex]
48/4 = 12
w^3/w = w^2
So our first term is 12w^2.
128/4 = 32
w^2/w = w
So our second term is 32w.
4w/4w = 1
Anything divided by itself is 1.
-1/4w, this can't be simplified further, so this is our last term.
So we have:
[tex]\sf 12w^2+32w+1-\dfrac{1}{4w}[/tex]
