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

Lösung

erweitern

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

\frac{x ^{3} + x ^{2} + 1}{x ^{10} + 3 x ^{8} + 3 x ^{6} + x ^{4} - x ^{7} - 3 x ^{5} - 3 x ^{3} - x}

Schritte zur Lösung

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

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

= \frac{x ^{3} + x ^{2} + 1}{x ( x - 1 ) ( x ^{2} + x + 1 ) ( x ^{6} + 3 x ^{4} + 3 x ^{2} + 1 )}

Multipliziere aus

x (x - 1) (x^{2} + x + 1) (x^{6} + 3 x^{4} + 3 x^{2} + 1) : x^{10} + 3 x^{8} + 3 x^{6} + x^{4} - x^{7} - 3 x^{5} - 3 x^{3} - x

= \frac{x ^{3} + x ^{2} + 1}{x ^{10} + 3 x ^{8} + 3 x ^{6} + x ^{4} - x ^{7} - 3 x ^{5} - 3 x ^{3} - x}

e x p an d (t^{2} + e^{t}) \cdot u \cdot (t - 3)

s im pl i f y (\frac{x - 6}{5} - \frac{3 x + 1}{7})^{2}

e x p an d \frac{1}{s ^{2} ( s ^{2} - 2 s + 5 )}

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

s im pl i f y (a + \frac{c - a}{6}) (1 + x^{2})