erweitern (6(-2+x^{4/3})(6+x^{4/3}))/(x^{5/3)}

Lösung

erweitern

\frac{6 ( - 2 + x ^{\frac{4}{3}} ) ( 6 + x ^{\frac{4}{3}} )}{x ^{\frac{5}{3}}}

- \frac{72}{x ^{\frac{5}{3}}} + \frac{24}{x ^{\frac{1}{3}}} + 6 x

Schritte zur Lösung

\frac{6 ( - 2 + x ^{\frac{4}{3}} ) ( 6 + x ^{\frac{4}{3}} )}{x ^{\frac{5}{3}}}

Multipliziere aus

6 (- 2 + x^{\frac{4}{3}}) (6 + x^{\frac{4}{3}}) : - 72 + 24 x^{\frac{4}{3}} + 6 x^{\frac{8}{3}}

= \frac{- 72 + 24 x ^{\frac{4}{3}} + 6 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}}

Wende Bruchregel an:

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

\frac{- 72 + 24 x ^{\frac{4}{3}} + 6 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}} = - \frac{72}{x ^{\frac{5}{3}}} + \frac{24 x ^{\frac{4}{3}}}{x ^{\frac{5}{3}}} + \frac{6 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}}

= - \frac{72}{x ^{\frac{5}{3}}} + \frac{24 x ^{\frac{4}{3}}}{x ^{\frac{5}{3}}} + \frac{6 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}}

Streiche

\frac{24 x ^{\frac{4}{3}}}{x ^{\frac{5}{3}}} : \frac{24}{x ^{\frac{1}{3}}}

= - \frac{72}{x ^{\frac{5}{3}}} + \frac{24}{x ^{\frac{1}{3}}} + \frac{6 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}}

Streiche

\frac{6 x ^{\frac{8}{3}}}{x ^{\frac{5}{3}}} : 6 x

= - \frac{72}{x ^{\frac{5}{3}}} + \frac{24}{x ^{\frac{1}{3}}} + 6 x

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