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

Lösung

erweitern

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

\frac{2 x ^{3} + 3 x ^{2} + x - 1}{x ^{5} + 5 x ^{4} + 12 x ^{3} + 16 x ^{2} + 12 x + 4}

Schritte zur Lösung

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

(x^{2} + 2 x + 2)^{2} = x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4

= \frac{2 x ^{3} + 3 x ^{2} + x - 1}{( x + 1 ) ( x ^{4} + 4 x ^{3} + 8 x ^{2} + 8 x + 4 )}

Multipliziere aus

(x + 1) (x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4) : x^{5} + 5 x^{4} + 12 x^{3} + 16 x^{2} + 12 x + 4

= \frac{2 x ^{3} + 3 x ^{2} + x - 1}{x ^{5} + 5 x ^{4} + 12 x ^{3} + 16 x ^{2} + 12 x + 4}

s im pl i f y (1 - u_{2 π} (t)) sin (t)

s im pl i f y (2 x - 3 y^{2}) (y^{2} - 3 z) (x^{\frac{11}{3}} - \frac{1}{y ^{\frac{1}{2}}})

e x p an d π (4 - x^{2})^{2}

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

e x p an d (19 sin (x) - 1) (19 sin (x) + 1)