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 (sin (x) cos (x) + 1)^{2}

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

s im pl i f y (- 1 + i)^{9}

s im pl i f y (- x y + \frac{5}{8}) (\frac{3}{4} - x y)

e x p an d (2 + 3 y + y^{2})^{5}