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

Lösung

erweitern

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

\frac{2 x ^{3} - 6 x ^{2} - 6 x - 2}{x ^{6} + 3 x ^{5} + 3 x ^{4} + x ^{3}}

Schritte zur Lösung

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

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

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

Multipliziere aus

x^{3} (x^{3} + 3 x^{2} + 3 x + 1) : x^{6} + 3 x^{5} + 3 x^{4} + x^{3}

= \frac{2 ( x ^{3} - 3 x ^{2} - 3 x - 1 )}{x ^{6} + 3 x ^{5} + 3 x ^{4} + x ^{3}}

Multipliziere aus

2 (x^{3} - 3 x^{2} - 3 x - 1) : 2 x^{3} - 6 x^{2} - 6 x - 2

= \frac{2 x ^{3} - 6 x ^{2} - 6 x - 2}{x ^{6} + 3 x ^{5} + 3 x ^{4} + x ^{3}}

e x p an d \frac{1}{( 12965 e - 3 \cdot s + 1 ) ^{3}}

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

e x p an d (e^{x} + e^{- x}) (e^{x} + e^{- x})

e x p an d \frac{ln ( s )}{s ( s + 1 )}

s im pl i f y (1 + x + 5)^{2}