erweitern-(2(-x^3-3x^2+9x+3))/((x^2+3)^3)

Lösung

erweitern

- \frac{2 ( - x ^{3} - 3 x ^{2} + 9 x + 3 )}{( x ^{2} + 3 ) ^{3}}

- \frac{- 2 x ^{3} - 6 x ^{2} + 18 x + 6}{x ^{6} + 9 x ^{4} + 27 x ^{2} + 27}

Schritte zur Lösung

- \frac{2 ( - x ^{3} - 3 x ^{2} + 9 x + 3 )}{( x ^{2} + 3 ) ^{3}}

(x^{2} + 3)^{3} = x^{6} + 9 x^{4} + 27 x^{2} + 27

= - \frac{2 ( - x ^{3} - 3 x ^{2} + 9 x + 3 )}{x ^{6} + 9 x ^{4} + 27 x ^{2} + 27}

Multipliziere aus

2 (- x^{3} - 3 x^{2} + 9 x + 3) : - 2 x^{3} - 6 x^{2} + 18 x + 6

= - \frac{- 2 x ^{3} - 6 x ^{2} + 18 x + 6}{x ^{6} + 9 x ^{4} + 27 x ^{2} + 27}

e x p an d (1 + \frac{1}{3} x)^{9}

e x p an d (5 - 1 + r) r

s im pl i f y (3 x - 5) (3 x - 3)

s im pl i f y (2 + 2) 4

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