erweitern ((pix+1)(3-x^2))/(x^3)

Lösung

erweitern

\frac{( π x + 1 ) ( 3 - x ^{2} )}{x ^{3}}

\frac{3 π}{x ^{2}} - π + \frac{3}{x ^{3}} - \frac{1}{x}

Schritte zur Lösung

\frac{( π x + 1 ) ( 3 - x ^{2} )}{x ^{3}}

Multipliziere aus

(π x + 1) (3 - x^{2}) : 3 π x - π x^{3} + 3 - x^{2}

= \frac{3 π x - π x ^{3} + 3 - x ^{2}}{x ^{3}}

Wende Bruchregel an:

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

\frac{3 π x - π x ^{3} + 3 - x ^{2}}{x ^{3}} = \frac{3 π x}{x ^{3}} - \frac{π x ^{3}}{x ^{3}} + \frac{3}{x ^{3}} - \frac{x ^{2}}{x ^{3}}

= \frac{3 π x}{x ^{3}} - \frac{π x ^{3}}{x ^{3}} + \frac{3}{x ^{3}} - \frac{x ^{2}}{x ^{3}}

Streiche

\frac{3 π x}{x ^{3}} : \frac{3 π}{x ^{2}}

= \frac{3 π}{x ^{2}} - \frac{π x ^{3}}{x ^{3}} + \frac{3}{x ^{3}} - \frac{x ^{2}}{x ^{3}}

Streiche

\frac{π x ^{3}}{x ^{3}} : π

= \frac{3 π}{x ^{2}} - π + \frac{3}{x ^{3}} - \frac{x ^{2}}{x ^{3}}

Streiche

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

= \frac{3 π}{x ^{2}} - π + \frac{3}{x ^{3}} - \frac{1}{x}

e x p an d d y (3 x^{2} + 5 = y)

e x p an d (2 + sin (e^{- b x} + 1))^{2}

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

e x p an d - \frac{5 ( 2 - x ^{\frac{1}{5}} ) ^{4}}{4}

e x p an d \frac{48}{( 2 s + 1 ) ( 4 s ^{2} + 4 s + 17 )}