erweitern ((2x^3-1)(4-3x))/((2x^2+1)^2)

Lösung

erweitern

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

\frac{8 x ^{3} - 6 x ^{4} - 4 + 3 x}{4 x ^{4} + 4 x ^{2} + 1}

Schritte zur Lösung

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

(2 x^{2} + 1)^{2} = 4 x^{4} + 4 x^{2} + 1

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

Multipliziere aus

(2 x^{3} - 1) (4 - 3 x) : 8 x^{3} - 6 x^{4} - 4 + 3 x

= \frac{8 x ^{3} - 6 x ^{4} - 4 + 3 x}{4 x ^{4} + 4 x ^{2} + 1}

e x p an d \frac{40 - 3 x}{x ^{2} ( x ^{2} - 9 x + 20 )}

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

e x p an d cos (t) U (t - π)

e x p an d \frac{( sec ^{2} ( x ) + 1 ) sec ^{2} ( x )}{1 + tan ^{3} ( x )}

e x p an d \frac{( u + ( u + a t ) ) t}{2}