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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

(4 x - 2)^{2} = 16 x^{2} - 16 x + 4

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{16 x ^{2}}{x ^{2}} : 16

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

Streiche

\frac{16 x}{x ^{2}} : \frac{16}{x}

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

e x p an d \frac{( - 24 x ^{2} + 12 x - 15 ) ( 4 x - 1 )}{16}

e x p an d (2 x - 3 y) (\frac{1}{2}, \frac{3}{2})

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

e x p an d 4 x y^{2} - 2 x y + \frac{( 4 x ^{2} y - x ^{2} - 5 ) d y}{d x}

f a c t or x^{4} (δ (x - 2)) d x