erweitern (3x^2-27x^4)/(x^3)

Lösung

erweitern

\frac{3 x ^{2} - 27 x ^{4}}{x ^{3}}

- 27 x + \frac{3}{x}

Schritte zur Lösung

\frac{3 x ^{2} - 27 x ^{4}}{x ^{3}}

Faktorisiere

3 x^{2} - 27 x^{4} : 3 x^{2} (1 - 9 x^{2})

= \frac{3 x ^{2} ( 1 - 9 x ^{2} )}{x ^{3}}

Streiche

\frac{3 x ^{2} ( 1 - 9 x ^{2} )}{x ^{3}} : \frac{3 ( - 9 x ^{2} + 1 )}{x}

= \frac{3 ( - 9 x ^{2} + 1 )}{x}

Multipliziere aus

3 (- 9 x^{2} + 1) : - 27 x^{2} + 3

= \frac{- 27 x ^{2} + 3}{x}

Wende Bruchregel an:

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

\frac{- 27 x ^{2} + 3}{x} = - \frac{27 x ^{2}}{x} + \frac{3}{x}

= - \frac{27 x ^{2}}{x} + \frac{3}{x}

Streiche

\frac{27 x ^{2}}{x} : 27 x

= - 27 x + \frac{3}{x}

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

e x p an d \frac{x ( 3000 - 3 x )}{2}

e x p an d \frac{1}{( S ( S + 1 ) ( 0.2 S + 1 ) )}

e x p an d (9 y^{8} + 2 x^{7} y) d x - (8 x y^{7} + x^{8}) d y

e x p an d sin^{(π \cdot (1 - t))} (x)