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

Lösung

erweitern

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

1 - \frac{4}{x} + \frac{5}{x ^{2}} - \frac{2}{x ^{3}}

Schritte zur Lösung

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

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

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

Multipliziere aus

(x^{2} - 2 x + 1) (x - 2) : x^{3} - 4 x^{2} + 5 x - 2

= \frac{x ^{3} - 4 x ^{2} + 5 x - 2}{x ^{3}}

Wende Bruchregel an:

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

\frac{x ^{3} - 4 x ^{2} + 5 x - 2}{x ^{3}} = \frac{x ^{3}}{x ^{3}} - \frac{4 x ^{2}}{x ^{3}} + \frac{5 x}{x ^{3}} - \frac{2}{x ^{3}}

= \frac{x ^{3}}{x ^{3}} - \frac{4 x ^{2}}{x ^{3}} + \frac{5 x}{x ^{3}} - \frac{2}{x ^{3}}

Wende Regel an

\frac{a}{a} = 1

\frac{x ^{3}}{x ^{3}} = 1

= 1 - \frac{4 x ^{2}}{x ^{3}} + \frac{5 x}{x ^{3}} - \frac{2}{x ^{3}}

Streiche

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

= 1 - \frac{4}{x} + \frac{5 x}{x ^{3}} - \frac{2}{x ^{3}}

Streiche

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

= 1 - \frac{4}{x} + \frac{5}{x ^{2}} - \frac{2}{x ^{3}}

e x p an d \frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5)

s im pl i f y (s + 2 + 23 j) (s + 2 - 23 j) (s + 12)

s im pl i f y (x - 5) \cdot (3 x + 6)

e x p an d (10 - 2) 3 + 5

e x p an d (1 + cos (t)) cos (\frac{t}{2}) + sin (t) sin (\frac{t}{2})