erweitern ((x^4-4)^2)/(16x^4)

Lösung

erweitern

\frac{( x ^{4} - 4 ) ^{2}}{16 x ^{4}}

\frac{x ^{4}}{16} - \frac{1}{2} + \frac{1}{x ^{4}}

Schritte zur Lösung

\frac{( x ^{4} - 4 ) ^{2}}{16 x ^{4}}

(x^{4} - 4)^{2} = x^{8} - 8 x^{4} + 16

= \frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}}

Wende Bruchregel an:

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

\frac{x ^{8} - 8 x ^{4} + 16}{16 x ^{4}} = \frac{x ^{8}}{16 x ^{4}} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{16}{16 x ^{4}}

= \frac{x ^{8}}{16 x ^{4}} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{16}{16 x ^{4}}

Streiche

\frac{x ^{8}}{16 x ^{4}} : \frac{x ^{4}}{16}

= \frac{x ^{4}}{16} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{16}{16 x ^{4}}

Streiche

\frac{8 x ^{4}}{16 x ^{4}} : \frac{1}{2}

= \frac{x ^{4}}{16} - \frac{1}{2} + \frac{16}{16 x ^{4}}

Teile die Zahlen:

\frac{16}{16} = 1

= \frac{x ^{4}}{16} - \frac{1}{2} + \frac{1}{x ^{4}}

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