erweitern (((t^4)-(10t^{3/2})))/((t^{9/2))}

Lösung

erweitern

\frac{( ( t ^{4} ) - ( 10 t ^{\frac{3}{2}} ) )}{( t ^{\frac{9}{2}} )}

\frac{1}{t ^{\frac{1}{2}}} - \frac{10}{t ^{3}}

Schritte zur Lösung

\frac{( t ^{4} ) - ( 10 t ^{\frac{3}{2}} )}{t ^{\frac{9}{2}}}

Entferne die Klammern:

(a) = a

= \frac{t ^{4} - 10 t ^{\frac{3}{2}}}{t ^{\frac{9}{2}}}

Wende Bruchregel an:

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

\frac{t ^{4} - 10 t ^{\frac{3}{2}}}{t ^{\frac{9}{2}}} = \frac{t ^{4}}{t ^{\frac{9}{2}}} - \frac{10 t ^{\frac{3}{2}}}{t ^{\frac{9}{2}}}

= \frac{t ^{4}}{t ^{\frac{9}{2}}} - \frac{10 t ^{\frac{3}{2}}}{t ^{\frac{9}{2}}}

Streiche

\frac{t ^{4}}{t ^{\frac{9}{2}}} : \frac{1}{t ^{\frac{1}{2}}}

= \frac{1}{t ^{\frac{1}{2}}} - \frac{10 t ^{\frac{3}{2}}}{t ^{\frac{9}{2}}}

Streiche

\frac{10 t ^{\frac{3}{2}}}{t ^{\frac{9}{2}}} : \frac{10}{t ^{3}}

= \frac{1}{t ^{\frac{1}{2}}} - \frac{10}{t ^{3}}

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