erweitern (5x^3+4x^2+7x+3)/((x^2+2x+2)(x^2-x-1))

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

e x p an d D x [3 6 x^{3} + 3 (5 x^{2} - 4)]

e x p an d (2 x^{2} + 3 x) (x - 1)

s im pl i f y x^{2} (x - \frac{1}{2})

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