erweitern (1+1/(s^2))((s^3)/2)

Lösung

erweitern

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

\frac{s ^{3}}{2} + \frac{s}{2}

Schritte zur Lösung

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

Apply rule:

(a) = a

(\frac{s ^{3}}{2}) = \frac{s ^{3}}{2}

= (1 + \frac{1}{s ^{2}}) \frac{s ^{3}}{2}

= \frac{s ^{3}}{2} (1 + \frac{1}{s ^{2}})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

\frac{s ^{3}}{2} (1 + \frac{1}{s ^{2}}) = \frac{s ^{3}}{2} \cdot 1 + \frac{s ^{3}}{2} \cdot \frac{1}{s ^{2}}

= \frac{s ^{3}}{2} \cdot 1 + \frac{s ^{3}}{2} \cdot \frac{1}{s ^{2}}

Vereinfache

\frac{s ^{3}}{2} \cdot 1 + \frac{s ^{3}}{2} \cdot \frac{1}{s ^{2}} : \frac{s ^{3}}{2} + \frac{s}{2}

= \frac{s ^{3}}{2} + \frac{s}{2}

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