erweitern (2(6-x^2)^2)/(x^2)

Lösung

erweitern

\frac{2 ( 6 - x ^{2} ) ^{2}}{x ^{2}}

\frac{72}{x ^{2}} - 24 + 2 x^{2}

Schritte zur Lösung

\frac{2 ( 6 - x ^{2} ) ^{2}}{x ^{2}}

(6 - x^{2})^{2} = 36 - 12 x^{2} + x^{4}

= \frac{2 ( x ^{4} - 12 x ^{2} + 36 )}{x ^{2}}

Multipliziere aus

2 (36 - 12 x^{2} + x^{4}) : 72 - 24 x^{2} + 2 x^{4}

= \frac{72 - 24 x ^{2} + 2 x ^{4}}{x ^{2}}

Wende Bruchregel an:

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

\frac{72 - 24 x ^{2} + 2 x ^{4}}{x ^{2}} = \frac{72}{x ^{2}} - \frac{24 x ^{2}}{x ^{2}} + \frac{2 x ^{4}}{x ^{2}}

= \frac{72}{x ^{2}} - \frac{24 x ^{2}}{x ^{2}} + \frac{2 x ^{4}}{x ^{2}}

Streiche

\frac{24 x ^{2}}{x ^{2}} : 24

= \frac{72}{x ^{2}} - 24 + \frac{2 x ^{4}}{x ^{2}}

Streiche

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

= \frac{72}{x ^{2}} - 24 + 2 x^{2}

e x p an d 2 π - 2 π x (2 - 2 x^{2})

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

e x p an d (\frac{1}{3 x} + (- 3) x^{2})^{8}

e x p an d (sec (x) - 1) cot (x) - csc (x)

e x p an d a sin ((n - 1) \frac{π}{2})