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

Lösung

erweitern

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

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

Schritte zur Lösung

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

(n^{2} - 9)^{2} = n^{4} - 18 n^{2} + 81

= \frac{n ^{4} - 18 n ^{2} + 81}{9 n ^{2}}

Wende Bruchregel an:

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

\frac{n ^{4} - 18 n ^{2} + 81}{9 n ^{2}} = \frac{n ^{4}}{9 n ^{2}} - \frac{18 n ^{2}}{9 n ^{2}} + \frac{81}{9 n ^{2}}

= \frac{n ^{4}}{9 n ^{2}} - \frac{18 n ^{2}}{9 n ^{2}} + \frac{81}{9 n ^{2}}

Streiche

\frac{n ^{4}}{9 n ^{2}} : \frac{n ^{2}}{9}

= \frac{n ^{2}}{9} - \frac{18 n ^{2}}{9 n ^{2}} + \frac{81}{9 n ^{2}}

Streiche

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

= \frac{n ^{2}}{9} - 2 + \frac{81}{9 n ^{2}}

Teile die Zahlen:

\frac{81}{9} = 9

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

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