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

Lösung

erweitern

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

x - 9 + \frac{27}{x} - \frac{27}{x ^{2}}

Schritte zur Lösung

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

(x - 3)^{3} = x^{3} - 9 x^{2} + 27 x - 27

= \frac{x ^{3} - 9 x ^{2} + 27 x - 27}{x ^{2}}

Wende Bruchregel an:

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

\frac{x ^{3} - 9 x ^{2} + 27 x - 27}{x ^{2}} = \frac{x ^{3}}{x ^{2}} - \frac{9 x ^{2}}{x ^{2}} + \frac{27 x}{x ^{2}} - \frac{27}{x ^{2}}

= \frac{x ^{3}}{x ^{2}} - \frac{9 x ^{2}}{x ^{2}} + \frac{27 x}{x ^{2}} - \frac{27}{x ^{2}}

Streiche

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

= x - \frac{9 x ^{2}}{x ^{2}} + \frac{27 x}{x ^{2}} - \frac{27}{x ^{2}}

Streiche

\frac{9 x ^{2}}{x ^{2}} : 9

= x - 9 + \frac{27 x}{x ^{2}} - \frac{27}{x ^{2}}

Streiche

\frac{27 x}{x ^{2}} : \frac{27}{x}

= x - 9 + \frac{27}{x} - \frac{27}{x ^{2}}

e x p an d x^{6} l e f t (x^{2} + 4 x)

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

s im pl i f y 1 + x (1 + x + 1 - x)

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

e x p an d (2 A x + B) e^{x} + e^{x} (A x^{2} + B x + C)