erweitern ((2x+7)(1-5x)(x+2))/(x(1-x)^2)

Lösung

erweitern

\frac{( 2 x + 7 ) ( 1 - 5 x ) ( x + 2 )}{x ( 1 - x ) ^{2}}

\frac{- 10 x ^{3} - 53 x ^{2} - 59 x + 14}{x - 2 x ^{2} + x ^{3}}

Schritte zur Lösung

\frac{( 2 x + 7 ) ( 1 - 5 x ) ( x + 2 )}{x ( 1 - x ) ^{2}}

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

= \frac{( 2 x + 7 ) ( - 5 x + 1 ) ( x + 2 )}{x ( x ^{2} - 2 x + 1 )}

Multipliziere aus

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

= \frac{( 2 x + 7 ) ( - 5 x + 1 ) ( x + 2 )}{x - 2 x ^{2} + x ^{3}}

Multipliziere aus

(2 x + 7) (1 - 5 x) (x + 2) : - 10 x^{3} - 53 x^{2} - 59 x + 14

= \frac{- 10 x ^{3} - 53 x ^{2} - 59 x + 14}{x - 2 x ^{2} + x ^{3}}

e x p an d \frac{14 !}{( 14 - 4 ) 4 !}

e x p an d (x - 3)^{\frac{5}{3}} (x + 2)

e x p an d 15 (x + 3 = 60)

s im pl i f y (r^{2} - 23)^{2}

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