What is expand ((1-e^{-at})z)/((z-1)(z-e^{-at))} ?

The solution to expand ((1-e^{-at})z)/((z-1)(z-e^{-at))} is (z-e^{-at}z)/(z^2-e^{-at)z-z+e^{-at}}

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expand ((1-e^{-at})z)/((z-1)(z-e^{-at))}

expand

\frac{( 1 - e ^{- a t} ) z}{( z - 1 ) ( z - e ^{- a t} )}

\frac{z - e ^{- a t} z}{z ^{2} - e ^{- a t} z - z + e ^{- a t}}

Solution steps

\frac{( 1 - e ^{- a t} ) z}{( z - 1 ) ( z - e ^{- a t} )}

Expand

(z - 1) (z - e^{- a t}) : z^{2} - e^{- a t} z - z + e^{- a t}

= \frac{z ( - e ^{- a t} + 1 )}{z ^{2} - e ^{- a t} z - z + e ^{- a t}}

Expand

(1 - e^{- a t}) z : z - e^{- a t} z

= \frac{z - e ^{- a t} z}{z ^{2} - e ^{- a t} z - z + e ^{- a t}}

(3 + h) - 2

\frac{1}{s ^{3} ( s - 1 ) ( s - 2 )}

\frac{4 ( 3 q - 10 )}{3}

\frac{4 x ^{2} + 2 x + 20}{x ( x ^{2} + 5 )}

(12 + 48 x^{2} + 16 x) e^{x^{2}}

What is expand ((1-e^{-at})z)/((z-1)(z-e^{-at))} ?
The solution to expand ((1-e^{-at})z)/((z-1)(z-e^{-at))} is (z-e^{-at}z)/(z^2-e^{-at)z-z+e^{-at}}