erweitern ((4-x^2)^3)/(8x^3)

Lösung

erweitern

\frac{( 4 - x ^{2} ) ^{3}}{8 x ^{3}}

\frac{8}{x ^{3}} - \frac{6}{x} + \frac{3 x}{2} - \frac{x ^{3}}{8}

Schritte zur Lösung

\frac{( 4 - x ^{2} ) ^{3}}{8 x ^{3}}

(4 - x^{2})^{3} = 64 - 48 x^{2} + 12 x^{4} - x^{6}

= \frac{64 - 48 x ^{2} + 12 x ^{4} - x ^{6}}{8 x ^{3}}

Wende Bruchregel an:

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

\frac{64 - 48 x ^{2} + 12 x ^{4} - x ^{6}}{8 x ^{3}} = \frac{64}{8 x ^{3}} - \frac{48 x ^{2}}{8 x ^{3}} + \frac{12 x ^{4}}{8 x ^{3}} - \frac{x ^{6}}{8 x ^{3}}

= \frac{64}{8 x ^{3}} - \frac{48 x ^{2}}{8 x ^{3}} + \frac{12 x ^{4}}{8 x ^{3}} - \frac{x ^{6}}{8 x ^{3}}

\frac{64}{8 x ^{3}} = \frac{8}{x ^{3}}

\frac{48 x ^{2}}{8 x ^{3}} = \frac{6}{x}

\frac{12 x ^{4}}{8 x ^{3}} = \frac{3 x}{2}

\frac{x ^{6}}{8 x ^{3}} = \frac{x ^{3}}{8}

= \frac{8}{x ^{3}} - \frac{6}{x} + \frac{3 x}{2} - \frac{x ^{3}}{8}

\frac{d ^{2}}{d x ^{2}} ((y) (- 6 x^{4} + 9))

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

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

e x p an d \frac{( 2 x - 3 ) ( 3 x - 1 )}{5 x ^{2} ( x - 5 )}

e x p an d (8, - 2) (2 x - 5 y = - 12)