erweitern-((t^2+1)^2)/(4t)

Lösung

erweitern

- \frac{( t ^{2} + 1 ) ^{2}}{4 t}

- \frac{t ^{3}}{4} - \frac{t}{2} - \frac{1}{4 t}

Schritte zur Lösung

- \frac{( t ^{2} + 1 ) ^{2}}{4 t}

(t^{2} + 1)^{2} = t^{4} + 2 t^{2} + 1

= - \frac{t ^{4} + 2 t ^{2} + 1}{4 t}

Wende Bruchregel an:

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

\frac{t ^{4} + 2 t ^{2} + 1}{4 t} = - (\frac{t ^{4}}{4 t}) - (\frac{2 t ^{2}}{4 t}) - (\frac{1}{4 t})

= - (\frac{t ^{4}}{4 t}) - (\frac{2 t ^{2}}{4 t}) - (\frac{1}{4 t})

Entferne die Klammern:

(a) = a

= - \frac{t ^{4}}{4 t} - \frac{2 t ^{2}}{4 t} - \frac{1}{4 t}

Streiche

\frac{t ^{4}}{4 t} : \frac{t ^{3}}{4}

= - \frac{t ^{3}}{4} - \frac{2 t ^{2}}{4 t} - \frac{1}{4 t}

Streiche

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

= - \frac{t ^{3}}{4} - \frac{t}{2} - \frac{1}{4 t}

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