\(\frac{\left(2z-1\right)^4}{\left(z\sqrt{z}+1\right)^4}\)this
is what you get okay now for the expansion.......
\(\frac{16z^4-32z^3+24z^2-8z+1}{z^6+4z^{\frac{9}{2}}+6z^3+4z\sqrt{z}+1}\)
i agree, the numbers are huge but u have your answer. multiply it out and you will get 1 as your constant term because of the +1 in your original equation