erweitern (x(-3x^4+10x^2-3))/(3(x^2+1)^6)

Lösung

erweitern

\frac{x ( - 3 x ^{4} + 10 x ^{2} - 3 )}{3 ( x ^{2} + 1 ) ^{6}}

\frac{- 3 x ^{5} + 10 x ^{3} - 3 x}{3 x ^{12} + 18 x ^{10} + 45 x ^{8} + 60 x ^{6} + 45 x ^{4} + 18 x ^{2} + 3}

Schritte zur Lösung

\frac{x ( - 3 x ^{4} + 10 x ^{2} - 3 )}{3 ( x ^{2} + 1 ) ^{6}}

(x^{2} + 1)^{6} = x^{12} + 6 x^{10} + 15 x^{8} + 20 x^{6} + 15 x^{4} + 6 x^{2} + 1

= \frac{x ( - 3 x ^{4} + 10 x ^{2} - 3 )}{3 ( x ^{12} + 6 x ^{10} + 15 x ^{8} + 20 x ^{6} + 15 x ^{4} + 6 x ^{2} + 1 )}

Multipliziere aus

3 (x^{12} + 6 x^{10} + 15 x^{8} + 20 x^{6} + 15 x^{4} + 6 x^{2} + 1) : 3 x^{12} + 18 x^{10} + 45 x^{8} + 60 x^{6} + 45 x^{4} + 18 x^{2} + 3

= \frac{x ( - 3 x ^{4} + 10 x ^{2} - 3 )}{3 x ^{12} + 18 x ^{10} + 45 x ^{8} + 60 x ^{6} + 45 x ^{4} + 18 x ^{2} + 3}

Multipliziere aus

x (- 3 x^{4} + 10 x^{2} - 3) : - 3 x^{5} + 10 x^{3} - 3 x

= \frac{- 3 x ^{5} + 10 x ^{3} - 3 x}{3 x ^{12} + 18 x ^{10} + 45 x ^{8} + 60 x ^{6} + 45 x ^{4} + 18 x ^{2} + 3}

e x p an d (y^{\frac{3}{4}} - 2 x^{\frac{3}{4}})^{4}

e x p an d \frac{1}{s ^{2} ( s ^{2} + 6 s + 9 )}

e x p an d \frac{( ( c + h ) sin ( \frac{1}{c + h} ) - ( c ) sin ( \frac{1}{c} ) )}{h}

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

e x p an d sin (u) (3 - 4 sin^{3} (u))