erweitern 1+((a^2(e^{x/a}+e^{-x/a})^2)/4)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

e x p an d \frac{( s + 1 ) ( s + 2 )}{s ( s + 3 ) ( s + 4 )}

e x p an d (1 - \frac{1}{x})^{4}

e x p an d \frac{( r _{1} r _{2} c + L ) ( 1 - w ^{2} L c )}{c ^{2} w}

e x p an d \frac{( a + 2 ) ! + a ! + ( a + 1 ) !}{( a + 2 ) \cdot a !}

e x p an d \frac{2 s ^{3} - 26 s ^{2} + 102 s - 124}{( s - 3 ) ^{3} ( s - 4 )}