erweitern ((5x^2-1)^3)/(30x)

Lösung

erweitern

\frac{( 5 x ^{2} - 1 ) ^{3}}{30 x}

\frac{25 x ^{5}}{6} - \frac{5 x ^{3}}{2} + \frac{x}{2} - \frac{1}{30 x}

Schritte zur Lösung

\frac{( 5 x ^{2} - 1 ) ^{3}}{30 x}

(5 x^{2} - 1)^{3} = 125 x^{6} - 75 x^{4} + 15 x^{2} - 1

= \frac{125 x ^{6} - 75 x ^{4} + 15 x ^{2} - 1}{30 x}

Wende Bruchregel an:

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

\frac{125 x ^{6} - 75 x ^{4} + 15 x ^{2} - 1}{30 x} = \frac{125 x ^{6}}{30 x} - \frac{75 x ^{4}}{30 x} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

= \frac{125 x ^{6}}{30 x} - \frac{75 x ^{4}}{30 x} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

Streiche

\frac{125 x ^{6}}{30 x} : \frac{25 x ^{5}}{6}

= \frac{25 x ^{5}}{6} - \frac{75 x ^{4}}{30 x} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

Streiche

\frac{75 x ^{4}}{30 x} : \frac{5 x ^{3}}{2}

= \frac{25 x ^{5}}{6} - \frac{5 x ^{3}}{2} + \frac{15 x ^{2}}{30 x} - \frac{1}{30 x}

Streiche

\frac{15 x ^{2}}{30 x} : \frac{x}{2}

= \frac{25 x ^{5}}{6} - \frac{5 x ^{3}}{2} + \frac{x}{2} - \frac{1}{30 x}

e x p an d 2 - x ((1 - x) (2 - x))

e x p an d e^{x + y} (- e^{- x - y} + e^{- x})

e x p an d \frac{3 ( a + b )}{z + 2 ( a + b )}

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

e x p an d - cos (3 (1 + 3 X^{2}))