erweitern (27x^{4/3}+3(x^3+5))/(x^{2/3)}

Lösung

erweitern

\frac{27 x ^{\frac{4}{3}} + 3 ( x ^{3} + 5 )}{x ^{\frac{2}{3}}}

27 x^{\frac{2}{3}} + 3 x^{\frac{7}{3}} + \frac{15}{x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{27 x ^{\frac{4}{3}} + 3 ( x ^{3} + 5 )}{x ^{\frac{2}{3}}}

Multipliziere aus

27 x^{\frac{4}{3}} + 3 (x^{3} + 5) : 27 x^{\frac{4}{3}} + 3 x^{3} + 15

= \frac{27 x ^{\frac{4}{3}} + 3 x ^{3} + 15}{x ^{\frac{2}{3}}}

Wende Bruchregel an:

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

\frac{27 x ^{\frac{4}{3}} + 3 x ^{3} + 15}{x ^{\frac{2}{3}}} = \frac{27 x ^{\frac{4}{3}}}{x ^{\frac{2}{3}}} + \frac{3 x ^{3}}{x ^{\frac{2}{3}}} + \frac{15}{x ^{\frac{2}{3}}}

= \frac{27 x ^{\frac{4}{3}}}{x ^{\frac{2}{3}}} + \frac{3 x ^{3}}{x ^{\frac{2}{3}}} + \frac{15}{x ^{\frac{2}{3}}}

Streiche

\frac{27 x ^{\frac{4}{3}}}{x ^{\frac{2}{3}}} : 27 x^{\frac{2}{3}}

= 27 x^{\frac{2}{3}} + \frac{3 x ^{3}}{x ^{\frac{2}{3}}} + \frac{15}{x ^{\frac{2}{3}}}

Streiche

\frac{3 x ^{3}}{x ^{\frac{2}{3}}} : 3 x^{\frac{7}{3}}

= 27 x^{\frac{2}{3}} + 3 x^{\frac{7}{3}} + \frac{15}{x ^{\frac{2}{3}}}

e x p an d (a - 3 e)^{2}

e x p an d (- 9 sin (t) + 9 sin (9 t))^{2}

e x p an d e^{- t} + (- 1 - e^{- t}) U (t - 5)

e x p an d 4.408904562 \cdot 1 0^{36}

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