erweitern ((x-2)^2)/(x^5)

Lösung

erweitern

\frac{( x - 2 ) ^{2}}{x ^{5}}

\frac{1}{x ^{3}} - \frac{4}{x ^{4}} + \frac{4}{x ^{5}}

Schritte zur Lösung

\frac{( x - 2 ) ^{2}}{x ^{5}}

(x - 2)^{2} = x^{2} - 4 x + 4

= \frac{x ^{2} - 4 x + 4}{x ^{5}}

Wende Bruchregel an:

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

\frac{x ^{2} - 4 x + 4}{x ^{5}} = \frac{x ^{2}}{x ^{5}} - \frac{4 x}{x ^{5}} + \frac{4}{x ^{5}}

= \frac{x ^{2}}{x ^{5}} - \frac{4 x}{x ^{5}} + \frac{4}{x ^{5}}

Streiche

\frac{x ^{2}}{x ^{5}} : \frac{1}{x ^{3}}

= \frac{1}{x ^{3}} - \frac{4 x}{x ^{5}} + \frac{4}{x ^{5}}

Streiche

\frac{4 x}{x ^{5}} : \frac{4}{x ^{4}}

= \frac{1}{x ^{3}} - \frac{4}{x ^{4}} + \frac{4}{x ^{5}}

e x p an d \frac{1}{x ( m - x )}

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

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

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

e x p an d 9 \cdot 895