erweitern ((t^2-6)^3)/(6t)

Lösung

erweitern

\frac{( t ^{2} - 6 ) ^{3}}{6 t}

\frac{t ^{5}}{6} - 3 t^{3} + 18 t - \frac{36}{t}

Schritte zur Lösung

\frac{( t ^{2} - 6 ) ^{3}}{6 t}

(t^{2} - 6)^{3} = t^{6} - 18 t^{4} + 108 t^{2} - 216

= \frac{t ^{6} - 18 t ^{4} + 108 t ^{2} - 216}{6 t}

Wende Bruchregel an:

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

\frac{t ^{6} - 18 t ^{4} + 108 t ^{2} - 216}{6 t} = \frac{t ^{6}}{6 t} - \frac{18 t ^{4}}{6 t} + \frac{108 t ^{2}}{6 t} - \frac{216}{6 t}

= \frac{t ^{6}}{6 t} - \frac{18 t ^{4}}{6 t} + \frac{108 t ^{2}}{6 t} - \frac{216}{6 t}

\frac{t ^{6}}{6 t} = \frac{t ^{5}}{6}

\frac{18 t ^{4}}{6 t} = 3 t^{3}

\frac{108 t ^{2}}{6 t} = 18 t

\frac{216}{6 t} = \frac{36}{t}

= \frac{t ^{5}}{6} - 3 t^{3} + 18 t - \frac{36}{t}

e x p an d (x y + y^{2} + x^{2}) d x - x^{2 d y = 0}

e x p an d \frac{2 ( x - 3 )}{x - 9}

e x p an d (1 + 6 x)^{4} (6) d x

e x p an d \frac{1}{( n - 1 ) ^{3}}

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