erweitern ((x^6-1)^2)/(4x^6)

Lösung

erweitern

\frac{( x ^{6} - 1 ) ^{2}}{4 x ^{6}}

\frac{x ^{6}}{4} - \frac{1}{2} + \frac{1}{4 x ^{6}}

Schritte zur Lösung

\frac{( x ^{6} - 1 ) ^{2}}{4 x ^{6}}

(x^{6} - 1)^{2} = x^{12} - 2 x^{6} + 1

= \frac{x ^{12} - 2 x ^{6} + 1}{4 x ^{6}}

Wende Bruchregel an:

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

\frac{x ^{12} - 2 x ^{6} + 1}{4 x ^{6}} = \frac{x ^{12}}{4 x ^{6}} - \frac{2 x ^{6}}{4 x ^{6}} + \frac{1}{4 x ^{6}}

= \frac{x ^{12}}{4 x ^{6}} - \frac{2 x ^{6}}{4 x ^{6}} + \frac{1}{4 x ^{6}}

Streiche

\frac{x ^{12}}{4 x ^{6}} : \frac{x ^{6}}{4}

= \frac{x ^{6}}{4} - \frac{2 x ^{6}}{4 x ^{6}} + \frac{1}{4 x ^{6}}

Streiche

\frac{2 x ^{6}}{4 x ^{6}} : \frac{1}{2}

= \frac{x ^{6}}{4} - \frac{1}{2} + \frac{1}{4 x ^{6}}

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