erweitern (20000(1-e^{-s}))/((s+100)^2)

Lösung

erweitern

\frac{20000 ( 1 - e ^{- s} )}{( s + 100 ) ^{2}}

\frac{20000 - 20000 e ^{- s}}{s ^{2} + 200 s + 10000}

Schritte zur Lösung

\frac{20000 ( 1 - e ^{- s} )}{( s + 100 ) ^{2}}

(s + 100)^{2} = s^{2} + 200 s + 10000

= \frac{20000 ( - e ^{- s} + 1 )}{s ^{2} + 200 s + 10000}

Multipliziere aus

20000 (1 - e^{- s}) : 20000 - 20000 e^{- s}

= \frac{20000 - 20000 e ^{- s}}{s ^{2} + 200 s + 10000}

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