erweitern ((1+2x)^3)/(x^4)

Lösung

erweitern

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

\frac{1}{x ^{4}} + \frac{6}{x ^{3}} + \frac{12}{x ^{2}} + \frac{8}{x}

Schritte zur Lösung

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

(1 + 2 x)^{3} = 1 + 6 x + 12 x^{2} + 8 x^{3}

= \frac{1 + 6 x + 12 x ^{2} + 8 x ^{3}}{x ^{4}}

Wende Bruchregel an:

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

\frac{1 + 6 x + 12 x ^{2} + 8 x ^{3}}{x ^{4}} = \frac{1}{x ^{4}} + \frac{6 x}{x ^{4}} + \frac{12 x ^{2}}{x ^{4}} + \frac{8 x ^{3}}{x ^{4}}

= \frac{1}{x ^{4}} + \frac{6 x}{x ^{4}} + \frac{12 x ^{2}}{x ^{4}} + \frac{8 x ^{3}}{x ^{4}}

Streiche

\frac{6 x}{x ^{4}} : \frac{6}{x ^{3}}

= \frac{1}{x ^{4}} + \frac{6}{x ^{3}} + \frac{12 x ^{2}}{x ^{4}} + \frac{8 x ^{3}}{x ^{4}}

Streiche

\frac{12 x ^{2}}{x ^{4}} : \frac{12}{x ^{2}}

= \frac{1}{x ^{4}} + \frac{6}{x ^{3}} + \frac{12}{x ^{2}} + \frac{8 x ^{3}}{x ^{4}}

Streiche

\frac{8 x ^{3}}{x ^{4}} : \frac{8}{x}

= \frac{1}{x ^{4}} + \frac{6}{x ^{3}} + \frac{12}{x ^{2}} + \frac{8}{x}

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

e x p an d e^{6 t} (6 e^{- 6 t} + C)

e x p an d \frac{5}{s ^{2} ( 2 s ^{2} + 1 )}

e x p an d \frac{981 ( 50 3 - 9 )}{400}

e x p an d \frac{9}{x ( 2 x - 3 ) ^{2}}