erweitern (((4x^4-1)^2)/(16x^4))+1

Lösung

erweitern

(\frac{( 4 x ^{4} - 1 ) ^{2}}{16 x ^{4}}) + 1

x^{4} - \frac{1}{2} + \frac{1}{16 x ^{4}} + 1

Schritte zur Lösung

(\frac{( 4 x ^{4} - 1 ) ^{2}}{16 x ^{4}}) + 1

Entferne die Klammern:

(a) = a

= \frac{( 4 x ^{4} - 1 ) ^{2}}{16 x ^{4}} + 1

(4 x^{4} - 1)^{2} = 16 x^{8} - 8 x^{4} + 1

= \frac{16 x ^{8} - 8 x ^{4} + 1}{16 x ^{4}} + 1

Wende Bruchregel an:

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

\frac{16 x ^{8} - 8 x ^{4} + 1}{16 x ^{4}} = \frac{16 x ^{8}}{16 x ^{4}} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{1}{16 x ^{4}}

= \frac{16 x ^{8}}{16 x ^{4}} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{1}{16 x ^{4}} + 1

Streiche

\frac{16 x ^{8}}{16 x ^{4}} : x^{4}

= x^{4} - \frac{8 x ^{4}}{16 x ^{4}} + \frac{1}{16 x ^{4}} + 1

Streiche

\frac{8 x ^{4}}{16 x ^{4}} : \frac{1}{2}

= x^{4} - \frac{1}{2} + \frac{1}{16 x ^{4}} + 1

e x p an d \frac{3 a ^{3} t}{( 7 a ^{2} + t ^{2} )}

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

e x p an d \frac{7 x ( x ^{2} + 9 )}{( 1 + 4 x ^{2} ) ( 4 - 5 x ^{3} )}

e x p an d 12 e^{2 t} \cdot (3 e^{2 t} + 6 t e^{2 t})

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