erweitern (3+sqrt(9-4k(3k-k^3)))/(2(3k-k^3))

Lösung

erweitern

\frac{3 + 9 - 4 k ( 3 k - k ^{3} )}{2 ( 3 k - k ^{3} )}

\frac{k}{3 - k ^{2}}

Schritte zur Lösung

\frac{3 + 9 - 4 k ( 3 k - k ^{3} )}{2 ( 3 k - k ^{3} )}

9 - 4 k (3 k - k^{3}) = (2 k + 3) (2 k - 3)

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

Multipliziere aus

2 (3 k - k^{3}) : 6 k - 2 k^{3}

= \frac{3 + ( 2 k + 3 ) ( 2 k - 3 )}{6 k - 2 k ^{3}}

Multipliziere aus

3 + (2 k + 3) (2 k - 3) : 2 k^{2}

= \frac{2 k ^{2}}{6 k - 2 k ^{3}}

Faktorisiere

6 k - 2 k^{3} : 2 k (3 - k^{2})

= \frac{2 k ^{2}}{2 k ( 3 - k ^{2} )}

Streiche

\frac{2 k ^{2}}{2 k ( 3 - k ^{2} )} : \frac{k}{3 - k ^{2}}

= \frac{k}{3 - k ^{2}}

e x p an d (36 e^{4 (t^{2} + 6 t)}) \cdot (2 t + 6)

\frac{d}{d t} ((m) (4 - 2 t))

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

e x p an d \frac{11 s + 10}{s ( s + 25 )}

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