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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

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

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

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

Wende Regel an

\frac{a}{a} = 1

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

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

Streiche

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

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

e x p an d - \frac{2 ( 4 - 10 )}{3}

e x p an d (x^{3} - y^{3}) d x + x y^{2} d y

e x p an d \frac{π ( - 60502 + 13520 \cdot 2 6 ^{\frac{1}{2}} )}{3}

e x p an d e^{4 x} (4 x - 16)

e x p an d lo g_{9} (23)