erweitern ((x-1)^3)/(x^2)

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

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

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

Streiche

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

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

Streiche

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

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

Streiche

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

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

e x p an d \frac{6}{( s ^{2} + 4 s + 20 ) ^{2}}

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

s im pl i f y (x + 3)^{2}

s im pl i f y (x + 2) (x - 2)

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