erweitern-(2(3x+1))/(x^3(x+1)^5)

Lösung

erweitern

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

- \frac{6 x + 2}{x ^{8} + 5 x ^{7} + 10 x ^{6} + 10 x ^{5} + 5 x ^{4} + x ^{3}}

Schritte zur Lösung

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

(x + 1)^{5} = x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1

= - \frac{2 ( 3 x + 1 )}{x ^{3} ( x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1 )}

Multipliziere aus

x^{3} (x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1) : x^{8} + 5 x^{7} + 10 x^{6} + 10 x^{5} + 5 x^{4} + x^{3}

= - \frac{2 ( 3 x + 1 )}{x ^{8} + 5 x ^{7} + 10 x ^{6} + 10 x ^{5} + 5 x ^{4} + x ^{3}}

Multipliziere aus

2 (3 x + 1) : 6 x + 2

= - \frac{6 x + 2}{x ^{8} + 5 x ^{7} + 10 x ^{6} + 10 x ^{5} + 5 x ^{4} + x ^{3}}

e x p an d 4 (\frac{w + 3}{2})^{2}

e x p an d \frac{\frac{d}{d x} ( - 4 x + 2 )}{( 3 x - 2 ) ^{2}}

\frac{d ^{3}}{d x ^{3}} ((y) (2 x^{7} - x^{4} - 3 x^{3}))

e x p an d \frac{( 9 x ^{2} - 3 ) ( x + 3 ) ( x ^{2} + 5 )}{x ^{4}}

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