erweitern (-3x^3+8x^2+24x-39)/((3x-2)^2(x^2+2x+5))

Lösung

erweitern

\frac{- 3 x ^{3} + 8 x ^{2} + 24 x - 39}{( 3 x - 2 ) ^{2} ( x ^{2} + 2 x + 5 )}

\frac{- 3 x ^{3} + 8 x ^{2} + 24 x - 39}{9 x ^{4} + 6 x ^{3} + 25 x ^{2} - 52 x + 20}

Schritte zur Lösung

\frac{- 3 x ^{3} + 8 x ^{2} + 24 x - 39}{( 3 x - 2 ) ^{2} ( x ^{2} + 2 x + 5 )}

(3 x - 2)^{2} = 9 x^{2} - 12 x + 4

= \frac{- 3 x ^{3} + 8 x ^{2} + 24 x - 39}{( 9 x ^{2} - 12 x + 4 ) ( x ^{2} + 2 x + 5 )}

Multipliziere aus

(9 x^{2} - 12 x + 4) (x^{2} + 2 x + 5) : 9 x^{4} + 6 x^{3} + 25 x^{2} - 52 x + 20

= \frac{- 3 x ^{3} + 8 x ^{2} + 24 x - 39}{9 x ^{4} + 6 x ^{3} + 25 x ^{2} - 52 x + 20}

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

e x p an d \frac{\frac{\partial}{\partial x} ( ( y - x ) ( x + y ) )}{2}

e x p an d \frac{1}{s ^{2} ( s + 10 )}

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

e x p an d \frac{( x - 1 ) ( x - 6 ) ( x - 5 )}{6}