erweitern ((ad-ec-ex)(-a-x))/e+(abd^2)/(e^2)

Lösung

erweitern

\frac{( a d - ec - e x ) ( - a - x )}{e} + \frac{ab d ^{2}}{e ^{2}}

- \frac{a ^{2} d}{e} - \frac{a d x}{e} + a c + c x + a x + x^{2} + \frac{a d ^{2} b}{e ^{2}}

Schritte zur Lösung

\frac{( a d - ec - e x ) ( - a - x )}{e} + \frac{ab d ^{2}}{e ^{2}}

Multipliziere aus

(a d - ec - e x) (- a - x) : - a^{2} d - a d x + e a c + ec x + e a x + e x^{2}

= \frac{e x ^{2} + ec x + e a x - a d x + e a c - a ^{2} d}{e} + \frac{a d ^{2} b}{e ^{2}}

Wende Bruchregel an:

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

\frac{- a ^{2} d - a d x + e a c + ec x + e a x + e x ^{2}}{e} = - \frac{a ^{2} d}{e} - \frac{a d x}{e} + \frac{e a c}{e} + \frac{ec x}{e} + \frac{e a x}{e} + \frac{e x ^{2}}{e}

= - \frac{a ^{2} d}{e} - \frac{a d x}{e} + \frac{e a c}{e} + \frac{ec x}{e} + \frac{e a x}{e} + \frac{e x ^{2}}{e} + \frac{a d ^{2} b}{e ^{2}}

\frac{e a c}{e} = a c

\frac{ec x}{e} = c x

\frac{e a x}{e} = a x

\frac{e x ^{2}}{e} = x^{2}

= - \frac{a ^{2} d}{e} - \frac{a d x}{e} + a c + c x + a x + x^{2} + \frac{a d ^{2} b}{e ^{2}}

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

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