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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

Streiche

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

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

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

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

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

s im pl i f y (5 - x) (5 + x)

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