erweitern (3x-9)/((x^3-1)(x-2)^3(x^2+x+1))

Lösung

erweitern

\frac{3 x - 9}{( x ^{3} - 1 ) ( x - 2 ) ^{3} ( x ^{2} + x + 1 )}

\frac{3 x - 9}{x ^{8} - 5 x ^{7} + 7 x ^{6} - 3 x ^{5} + 9 x ^{4} - 15 x ^{3} + 2 x ^{2} - 4 x + 8}

Schritte zur Lösung

\frac{3 x - 9}{( x ^{3} - 1 ) ( x - 2 ) ^{3} ( x ^{2} + x + 1 )}

(x - 2)^{3} = x^{3} - 6 x^{2} + 12 x - 8

= \frac{3 x - 9}{( x ^{3} - 1 ) ( x ^{3} - 6 x ^{2} + 12 x - 8 ) ( x ^{2} + x + 1 )}

Multipliziere aus

(x^{3} - 1) (x^{3} - 6 x^{2} + 12 x - 8) (x^{2} + x + 1) : x^{8} - 5 x^{7} + 7 x^{6} - 3 x^{5} + 9 x^{4} - 15 x^{3} + 2 x^{2} - 4 x + 8

= \frac{3 x - 9}{x ^{8} - 5 x ^{7} + 7 x ^{6} - 3 x ^{5} + 9 x ^{4} - 15 x ^{3} + 2 x ^{2} - 4 x + 8}

e x p an d \frac{2 x ( x - 3 )}{x ^{3} - x ^{2} - 6}

e x p an d \frac{1}{( x + 5 ) ( x + 4 )}

e x p an d (5 x + 8 y = 11, 5) (3 x + 5 y = 70)

e x p an d \frac{s + 2}{( s + 1 ) ( s ^{2} + 4 )}

s im pl i f y 4 x^{2} \cdot (\frac{15}{x} - \frac{2 x}{5})