erweitern ((a^2+4)*(3a^2-4))/(4a^2)

Lösung

erweitern

\frac{( a ^{2} + 4 ) \cdot ( 3 a ^{2} - 4 )}{4 a ^{2}}

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

Schritte zur Lösung

\frac{( a ^{2} + 4 ) ( 3 a ^{2} - 4 )}{4 a ^{2}}

Multipliziere aus

(a^{2} + 4) (3 a^{2} - 4) : 3 a^{4} + 8 a^{2} - 16

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

Streiche

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

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

Teile die Zahlen:

\frac{16}{4} = 4

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

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

e x p an d 2 π (\frac{π}{8} ln (2) - \frac{3}{4})

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

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

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