erweitern ((v-1)(v^2+v+1))/(v^2)

Lösung

erweitern

\frac{( v - 1 ) ( v ^{2} + v + 1 )}{v ^{2}}

v - \frac{1}{v ^{2}}

Schritte zur Lösung

\frac{( v - 1 ) ( v ^{2} + v + 1 )}{v ^{2}}

Multipliziere aus

(v - 1) (v^{2} + v + 1) : v^{3} - 1

= \frac{v ^{3} - 1}{v ^{2}}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{v ^{3} - 1}{v ^{2}} = \frac{v ^{3}}{v ^{2}} - \frac{1}{v ^{2}}

= \frac{v ^{3}}{v ^{2}} - \frac{1}{v ^{2}}

Streiche

\frac{v ^{3}}{v ^{2}} : v

= v - \frac{1}{v ^{2}}

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