erweitern ((e^{x/a}-e^{-x/a})^2)/4

Lösung

erweitern

\frac{( e ^{\frac{x}{a}} - e ^{- \frac{x}{a}} ) ^{2}}{4}

\frac{e ^{\frac{2 x}{a}}}{4} - \frac{1}{2} + \frac{e ^{- \frac{2 x}{a}}}{4}

Schritte zur Lösung

\frac{( e ^{\frac{x}{a}} - e ^{- \frac{x}{a}} ) ^{2}}{4}

(e^{\frac{x}{a}} - e^{- \frac{x}{a}})^{2} = e^{\frac{2 x}{a}} - 2 + e^{- \frac{2 x}{a}}

= \frac{e ^{\frac{2 x}{a}} - 2 + e ^{- \frac{2 x}{a}}}{4}

Wende Bruchregel an:

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

\frac{e ^{\frac{2 x}{a}} - 2 + e ^{- \frac{2 x}{a}}}{4} = \frac{e ^{\frac{2 x}{a}}}{4} - \frac{2}{4} + \frac{e ^{- \frac{2 x}{a}}}{4}

= \frac{e ^{\frac{2 x}{a}}}{4} - \frac{2}{4} + \frac{e ^{- \frac{2 x}{a}}}{4}

Streiche

\frac{2}{4} : \frac{1}{2}

= \frac{e ^{\frac{2 x}{a}}}{4} - \frac{1}{2} + \frac{e ^{- \frac{2 x}{a}}}{4}

e x p an d \frac{10 s + 4}{s ( s + 1 ) ( s ^{2} + 4 s + 5 )}

e x p an d e^{2} (y + 2 z) d z

e x p an d (3 x - 1) (2 x e^{3} + 4 x^{2} - 5)

e x p an d \frac{( 1 + sin ( x ) ) ^{2}}{2}

e x p an d \frac{5 z ^{2} ( z + 2 )}{3 z - 1}