erweitern ((y^2+1)(y^4-y^2+1))/(2y^3)

Lösung

erweitern

\frac{( y ^{2} + 1 ) ( y ^{4} - y ^{2} + 1 )}{2 y ^{3}}

\frac{y ^{3}}{2} + \frac{1}{2 y ^{3}}

Schritte zur Lösung

\frac{( y ^{2} + 1 ) ( y ^{4} - y ^{2} + 1 )}{2 y ^{3}}

Multipliziere aus

(y^{2} + 1) (y^{4} - y^{2} + 1) : y^{6} + 1

= \frac{y ^{6} + 1}{2 y ^{3}}

Wende Bruchregel an:

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

\frac{y ^{6} + 1}{2 y ^{3}} = \frac{y ^{6}}{2 y ^{3}} + \frac{1}{2 y ^{3}}

= \frac{y ^{6}}{2 y ^{3}} + \frac{1}{2 y ^{3}}

Streiche

\frac{y ^{6}}{2 y ^{3}} : \frac{y ^{3}}{2}

= \frac{y ^{3}}{2} + \frac{1}{2 y ^{3}}

e x p an d - \frac{120}{( 3 - 1 ) ^{6}} - cos (3 - 1)

e x p an d (3 tan^{2} (x) - 1) (tan^{2} (x) - 3)

e x p an d (x - 2 i) (x + 2 i)

e x p an d (x^{\frac{2}{3}} - 1)^{2}

e x p an d cot (x) + cos (x) (tan (x) - tan (\frac{x}{2}))