erweitern (6x^3+14x^2+x-12)/(x(x-1)(x+2)^2)

Lösung

erweitern

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x + 2 ) ^{2}}

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ^{4} + 3 x ^{3} - 4 x}

Schritte zur Lösung

\frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x + 2 ) ^{2}}

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

= \frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ( x - 1 ) ( x ^{2} + 4 x + 4 )}

Multipliziere aus

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

= \frac{6 x ^{3} + 14 x ^{2} + x - 12}{x ^{4} + 3 x ^{3} - 4 x}

s im pl i f y \frac{1}{3} + \frac{2}{9} (1.1 - 1)

e x p an d \frac{3 x}{( x - 2 ) ( x ^{2} + 5 ) ^{3}}

e x p an d cos (x) (csc (x) - sec (x))

e x p an d (\frac{x}{2} + \frac{1}{x})^{12}

e x p an d \frac{x ^{9} + 5 x ^{5} - x ^{3} + 2021}{x ^{3} ( x ^{4} - 16 )}