erweitern-(9(n+1)(2n+1))/(2n^2)

Lösung

erweitern

- \frac{9 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

- 9 - \frac{27}{2 n} - \frac{9}{2 n ^{2}}

Schritte zur Lösung

- \frac{9 ( n + 1 ) ( 2 n + 1 )}{2 n ^{2}}

Multipliziere aus

9 (n + 1) (2 n + 1) : 18 n^{2} + 27 n + 9

= - \frac{18 n ^{2} + 27 n + 9}{2 n ^{2}}

Wende Bruchregel an:

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

\frac{18 n ^{2} + 27 n + 9}{2 n ^{2}} = - (\frac{18 n ^{2}}{2 n ^{2}}) - (\frac{27 n}{2 n ^{2}}) - (\frac{9}{2 n ^{2}})

= - (\frac{18 n ^{2}}{2 n ^{2}}) - (\frac{27 n}{2 n ^{2}}) - (\frac{9}{2 n ^{2}})

Entferne die Klammern:

(a) = a

= - \frac{18 n ^{2}}{2 n ^{2}} - \frac{27 n}{2 n ^{2}} - \frac{9}{2 n ^{2}}

Streiche

\frac{18 n ^{2}}{2 n ^{2}} : 9

= - 9 - \frac{27 n}{2 n ^{2}} - \frac{9}{2 n ^{2}}

Streiche

\frac{27 n}{2 n ^{2}} : \frac{27}{2 n}

= - 9 - \frac{27}{2 n} - \frac{9}{2 n ^{2}}

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