erweitern (x^5-3x^2+12x-1)/(x^3(x^2+x+1)(x+2)^3)

Lösung

erweitern

\frac{x ^{5} - 3 x ^{2} + 12 x - 1}{x ^{3} ( x ^{2} + x + 1 ) ( x + 2 ) ^{3}}

\frac{x ^{5} - 3 x ^{2} + 12 x - 1}{x ^{8} + 7 x ^{7} + 19 x ^{6} + 26 x ^{5} + 20 x ^{4} + 8 x ^{3}}

Schritte zur Lösung

\frac{x ^{5} - 3 x ^{2} + 12 x - 1}{x ^{3} ( x ^{2} + x + 1 ) ( x + 2 ) ^{3}}

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

= \frac{x ^{5} - 3 x ^{2} + 12 x - 1}{x ^{3} ( x ^{2} + x + 1 ) ( x ^{3} + 6 x ^{2} + 12 x + 8 )}

Multipliziere aus

x^{3} (x^{2} + x + 1) (x^{3} + 6 x^{2} + 12 x + 8) : x^{8} + 7 x^{7} + 19 x^{6} + 26 x^{5} + 20 x^{4} + 8 x^{3}

= \frac{x ^{5} - 3 x ^{2} + 12 x - 1}{x ^{8} + 7 x ^{7} + 19 x ^{6} + 26 x ^{5} + 20 x ^{4} + 8 x ^{3}}

e x p an d (- 2 sin (x) - sin (2 x) \cdot 2)^{2}

s im pl i f y (x + 1 + 2 x) (3 x + 1 - x)

e x p an d 5 (3 - x) e^{x}

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

e x p an d (t - 4) sin (2 (t - 4) H (t - 4))