erweitern ((n^2-36)^2)/(36n^2)

Lösung

erweitern

\frac{( n ^{2} - 36 ) ^{2}}{36 n ^{2}}

\frac{n ^{2}}{36} - 2 + \frac{36}{n ^{2}}

Schritte zur Lösung

\frac{( n ^{2} - 36 ) ^{2}}{36 n ^{2}}

(n^{2} - 36)^{2} = n^{4} - 72 n^{2} + 1296

= \frac{n ^{4} - 72 n ^{2} + 1296}{36 n ^{2}}

Wende Bruchregel an:

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

\frac{n ^{4} - 72 n ^{2} + 1296}{36 n ^{2}} = \frac{n ^{4}}{36 n ^{2}} - \frac{72 n ^{2}}{36 n ^{2}} + \frac{1296}{36 n ^{2}}

= \frac{n ^{4}}{36 n ^{2}} - \frac{72 n ^{2}}{36 n ^{2}} + \frac{1296}{36 n ^{2}}

Streiche

\frac{n ^{4}}{36 n ^{2}} : \frac{n ^{2}}{36}

= \frac{n ^{2}}{36} - \frac{72 n ^{2}}{36 n ^{2}} + \frac{1296}{36 n ^{2}}

Streiche

\frac{72 n ^{2}}{36 n ^{2}} : 2

= \frac{n ^{2}}{36} - 2 + \frac{1296}{36 n ^{2}}

Teile die Zahlen:

\frac{1296}{36} = 36

= \frac{n ^{2}}{36} - 2 + \frac{36}{n ^{2}}

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