erweitern-(x^3+6x^2+16x-32)/(2(x+4)^2(x^2+16))

Lösung

erweitern

- \frac{x ^{3} + 6 x ^{2} + 16 x - 32}{2 ( x + 4 ) ^{2} ( x ^{2} + 16 )}

- \frac{x ^{3} + 6 x ^{2} + 16 x - 32}{2 x ^{4} + 64 x ^{2} + 16 x ^{3} + 256 x + 512}

Schritte zur Lösung

- \frac{x ^{3} + 6 x ^{2} + 16 x - 32}{2 ( x + 4 ) ^{2} ( x ^{2} + 16 )}

(x + 4)^{2} = x^{2} + 8 x + 16

= - \frac{x ^{3} + 6 x ^{2} + 16 x - 32}{2 ( x ^{2} + 8 x + 16 ) ( x ^{2} + 16 )}

Multipliziere aus

2 (x^{2} + 8 x + 16) (x^{2} + 16) : 2 x^{4} + 64 x^{2} + 16 x^{3} + 256 x + 512

= - \frac{x ^{3} + 6 x ^{2} + 16 x - 32}{2 x ^{4} + 16 x ^{3} + 64 x ^{2} + 256 x + 512}

e x p an d (y + Δ y)^{3}

s im pl i f y (6 x - 7) (9 x + 5)

s im pl i f y 2 (- \frac{1}{6} csc^{6} (\frac{x}{2}) + \frac{1}{4} csc^{4} (\frac{x}{2})) + C

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

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