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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

(2 x^{2} + 2 x + 1) (2 x^{2} - 2 x + 1) : 4 x^{4} + 1

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

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

e x p an d \frac{( x + h ) ^{3} - 3 a x ^{2} + 2 b x + c}{h}

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

e x p an d \frac{1}{2 ( cosh ( x ) + cos ( x ) )}

e x p an d (3 - 11 - x) (6 - x + 2)