erweitern ((x^2+1)(x^2-2))/(x^{2/3)}

Lösung

erweitern

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

x^{\frac{10}{3}} - x^{\frac{4}{3}} - \frac{2}{x ^{\frac{2}{3}}}

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{x ^{4}}{x ^{\frac{2}{3}}} : x^{\frac{10}{3}}

= x^{\frac{10}{3}} - \frac{x ^{2}}{x ^{\frac{2}{3}}} - \frac{2}{x ^{\frac{2}{3}}}

Streiche

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

= x^{\frac{10}{3}} - x^{\frac{4}{3}} - \frac{2}{x ^{\frac{2}{3}}}

e x p an d \frac{x - 4}{3 x ^{2}}

e x p an d \frac{- 1 + 4 a}{3 ( - 1 + a )}

e x p an d 1 + x^{- 2}

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

e x p an d ln (\frac{x ^{3} y}{z ^{5}})