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

Lösung

erweitern

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

\frac{x ^{3}}{x ^{8} + 5 x ^{7} + 12 x ^{6} + 26 x ^{5} + 37 x ^{4} + 21 x ^{3} + 6 x ^{2} - 36 x - 72}

Schritte zur Lösung

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

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

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

(x^{2} + 3)^{2} = x^{4} + 6 x^{2} + 9

= \frac{x ^{3}}{( x - 1 ) ( x ^{3} + 6 x ^{2} + 12 x + 8 ) ( x ^{4} + 6 x ^{2} + 9 )}

Multipliziere aus

(x - 1) (x^{3} + 6 x^{2} + 12 x + 8) (x^{4} + 6 x^{2} + 9) : x^{8} + 5 x^{7} + 12 x^{6} + 26 x^{5} + 37 x^{4} + 21 x^{3} + 6 x^{2} - 36 x - 72

= \frac{x ^{3}}{x ^{8} + 5 x ^{7} + 12 x ^{6} + 26 x ^{5} + 37 x ^{4} + 21 x ^{3} + 6 x ^{2} - 36 x - 72}

s im pl i f y (cos (A) + 1) (cos (A) - 1)

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

s im pl i f y (x + i y)^{2} (x - i y)

e x p an d (x^{3} + y^{3}) d x

e x p an d \frac{2 x ^{2} + 1}{( x - 3 ) ^{2}}