s$)$ Suppose that the algebraic expression for the $z-$transform of $x[n]$

$x(z)=\frac{1-\frac{1}{4}{z}^{-2}}{(1+\frac{1}{4}{z}^{-2})(1+\frac{5}{4}{z}^{-1}+\frac{3}{8}{z}^{-2})}$