erweitern ((n^2-25)^2)/(25n^2)

Lösung

erweitern

\frac{( n ^{2} - 25 ) ^{2}}{25 n ^{2}}

\frac{n ^{2}}{25} - 2 + \frac{25}{n ^{2}}

Schritte zur Lösung

\frac{( n ^{2} - 25 ) ^{2}}{25 n ^{2}}

(n^{2} - 25)^{2} = n^{4} - 50 n^{2} + 625

= \frac{n ^{4} - 50 n ^{2} + 625}{25 n ^{2}}

Wende Bruchregel an:

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

\frac{n ^{4} - 50 n ^{2} + 625}{25 n ^{2}} = \frac{n ^{4}}{25 n ^{2}} - \frac{50 n ^{2}}{25 n ^{2}} + \frac{625}{25 n ^{2}}

= \frac{n ^{4}}{25 n ^{2}} - \frac{50 n ^{2}}{25 n ^{2}} + \frac{625}{25 n ^{2}}

Streiche

\frac{n ^{4}}{25 n ^{2}} : \frac{n ^{2}}{25}

= \frac{n ^{2}}{25} - \frac{50 n ^{2}}{25 n ^{2}} + \frac{625}{25 n ^{2}}

Streiche

\frac{50 n ^{2}}{25 n ^{2}} : 2

= \frac{n ^{2}}{25} - 2 + \frac{625}{25 n ^{2}}

Teile die Zahlen:

\frac{625}{25} = 25

= \frac{n ^{2}}{25} - 2 + \frac{25}{n ^{2}}

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