erweitern (2(u-1)^3)/u

Lösung

erweitern

\frac{2 ( u - 1 ) ^{3}}{u}

2 u^{2} - 6 u + 6 - \frac{2}{u}

Schritte zur Lösung

\frac{2 ( u - 1 ) ^{3}}{u}

(u - 1)^{3} = u^{3} - 3 u^{2} + 3 u - 1

= \frac{2 ( u ^{3} - 3 u ^{2} + 3 u - 1 )}{u}

Multipliziere aus

2 (u^{3} - 3 u^{2} + 3 u - 1) : 2 u^{3} - 6 u^{2} + 6 u - 2

= \frac{2 u ^{3} - 6 u ^{2} + 6 u - 2}{u}

Wende Bruchregel an:

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

\frac{2 u ^{3} - 6 u ^{2} + 6 u - 2}{u} = \frac{2 u ^{3}}{u} - \frac{6 u ^{2}}{u} + \frac{6 u}{u} - \frac{2}{u}

= \frac{2 u ^{3}}{u} - \frac{6 u ^{2}}{u} + \frac{6 u}{u} - \frac{2}{u}

Streiche

\frac{2 u ^{3}}{u} : 2 u^{2}

= 2 u^{2} - \frac{6 u ^{2}}{u} + \frac{6 u}{u} - \frac{2}{u}

Streiche

\frac{6 u ^{2}}{u} : 6 u

= 2 u^{2} - 6 u + \frac{6 u}{u} - \frac{2}{u}

Streiche

\frac{6 u}{u} : 6

= 2 u^{2} - 6 u + 6 - \frac{2}{u}

e x p an d \frac{x ^{2} + 2 x + 4}{( x ^{2} + 4 ) ( x + 2 )}

e x p an d e^{x} (sin (y) + cos (y))

e x p an d \frac{2 x ^{2} + 1}{x ( x ^{2} - 9 ) ( x ^{2} + 9 )}

e x p an d \frac{( x - y ) ^{3}}{( y - z ) ^{2}}

e x p an d \frac{( - 3 x + 8 )}{2 ( x - 2 )}