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

Lösung

erweitern

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

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

Schritte zur Lösung

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

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{x ^{3}}{x ^{4}} : \frac{1}{x}

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

Streiche

\frac{3 x ^{2}}{x ^{4}} : \frac{3}{x ^{2}}

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

Streiche

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

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

e x p an d \frac{2 \cdot 5 + 4}{5 - 5}

e x p an d ((3 - 6 sin (θ))^{2}) d θ

e x p an d (2 a - 3 e) (4 a^{2} + 6 a e + 9 e)

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

e x p an d \frac{1}{3} (8 x - 9 y = 2)