erweitern ((e^8-1)^2)/(4e^8)

Lösung

erweitern

\frac{( e ^{8} - 1 ) ^{2}}{4 e ^{8}}

\frac{e ^{8}}{4} - \frac{1}{2} + \frac{1}{4 e ^{8}}

Dezimale

744.73958 \dots

Schritte zur Lösung

\frac{( e ^{8} - 1 ) ^{2}}{4 e ^{8}}

(e^{8} - 1)^{2} = e^{16} - 2 e^{8} + 1

= \frac{e ^{16} - 2 e ^{8} + 1}{4 e ^{8}}

Wende Bruchregel an:

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

\frac{e ^{16} - 2 e ^{8} + 1}{4 e ^{8}} = \frac{e ^{16}}{4 e ^{8}} - \frac{2 e ^{8}}{4 e ^{8}} + \frac{1}{4 e ^{8}}

= \frac{e ^{16}}{4 e ^{8}} - \frac{2 e ^{8}}{4 e ^{8}} + \frac{1}{4 e ^{8}}

Streiche

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

= \frac{e ^{8}}{4} - \frac{2 e ^{8}}{4 e ^{8}} + \frac{1}{4 e ^{8}}

Streiche

\frac{2 e ^{8}}{4 e ^{8}} : \frac{1}{2}

= \frac{e ^{8}}{4} - \frac{1}{2} + \frac{1}{4 e ^{8}}

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