erweitern ((sqrt(a^2-4))^4sqrt(a^2-4))/a

Lösung

erweitern

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

a^{3} a^{2} - 4 - 8 a a^{2} - 4 + \frac{16 a ^{2} - 4}{a}

Schritte zur Lösung

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

(a^{2} - 4)^{4} = a^{4} - 8 a^{2} + 16

= \frac{( a ^{4} - 8 a ^{2} + 16 ) a ^{2} - 4}{a}

Multipliziere aus

(a^{4} - 8 a^{2} + 16) a^{2} - 4 : a^{4} a^{2} - 4 - 8 a^{2} a^{2} - 4 + 16 a^{2} - 4

= \frac{a ^{4} a ^{2} - 4 - 8 a ^{2} a ^{2} - 4 + 16 a ^{2} - 4}{a}

Wende Bruchregel an:

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

\frac{a ^{4} a ^{2} - 4 - 8 a ^{2} a ^{2} - 4 + 16 a ^{2} - 4}{a} = \frac{a ^{4} a ^{2} - 4}{a} - \frac{8 a ^{2} a ^{2} - 4}{a} + \frac{16 a ^{2} - 4}{a}

= \frac{a ^{4} a ^{2} - 4}{a} - \frac{8 a ^{2} a ^{2} - 4}{a} + \frac{16 a ^{2} - 4}{a}

Streiche

\frac{a ^{4} a ^{2} - 4}{a} : a^{3} a^{2} - 4

= a^{3} a^{2} - 4 - \frac{8 a ^{2} a ^{2} - 4}{a} + \frac{16 a ^{2} - 4}{a}

Streiche

\frac{8 a ^{2} a ^{2} - 4}{a} : 8 a a^{2} - 4

= a^{3} a^{2} - 4 - 8 a a^{2} - 4 + \frac{16 a ^{2} - 4}{a}

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

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

e x p an d lo g_{10} (\frac{x y ^{2}}{2 m})

e x p an d \frac{d}{d y} ((x y^{2} - 1) e^{x}) - y^{2} e^{x}

e x p an d \frac{\partial}{\partial x} (x^{2}) + 2 y + λ (x - 2 y)