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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

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}}

Streiche

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

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

Streiche

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

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

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

e x p an d \frac{4 x ^{2} + 16 x - 21}{( x + 2 ) ^{2}}

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

e x p an d e^{s} (1 - e^{- s})

e x p an d \frac{( s + 5 )}{( s + 8 ) ( s - 3 )}