What is the inverse of+(z^{-1})/((1-0.5*z^{-1))^2} ?

The inverse of+(z^{-1})/((1-0.5*z^{-1))^2} is (z+1+sqrt(2z+1))/(2z),(z+1-sqrt(2z+1))/(2z)

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inverse of+(z^{-1})/((1-0.5*z^{-1))^2}

inverse

+ \frac{z ^{- 1}}{( 1 - 0.5 \cdot z ^{- 1} ) ^{2}}

\frac{z + 1 + 2 z + 1}{2 z}, \frac{z + 1 - 2 z + 1}{2 z}

Solution steps

y = \frac{z ^{- 1}}{( 1 - 0.5 z ^{- 1} ) ^{2}}

Replace

z

with

y

z = \frac{y ^{- 1}}{( 1 - 0.5 y ^{- 1} ) ^{2}}

Solve for

y, z = + \frac{y ^{- 1}}{( 1 - 0.5 \cdot y ^{- 1} ) ^{2}}

\frac{z + 1 + 2 z + 1}{2 z}, \frac{z + 1 - 2 z + 1}{2 z}

What is the inverse of+(z^{-1})/((1-0.5*z^{-1))^2} ?
The inverse of+(z^{-1})/((1-0.5*z^{-1))^2} is (z+1+sqrt(2z+1))/(2z),(z+1-sqrt(2z+1))/(2z)