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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Multipliziere aus

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

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

e x p an d (4 - cos^{2} (t))^{2}

\frac{d}{d t} ((x) (1 + t))

e x p an d \frac{4 ( 3 x ^{2} + 4 )}{( x ^{2} - 4 ) ^{3}}

e x p an d (x - a) (x - b) (x - c) (x - d) (x - e)

e x p an d \frac{1}{2 k ( 4 - 8 k + 20 k ^{2} )}