erweitern (12x^3-37x^2+48x-36)/((x-2)^2(x^2+4))

Lösung

erweitern

\frac{12 x ^{3} - 37 x ^{2} + 48 x - 36}{( x - 2 ) ^{2} ( x ^{2} + 4 )}

\frac{12 x ^{3} - 37 x ^{2} + 48 x - 36}{x ^{4} + 8 x ^{2} - 4 x ^{3} - 16 x + 16}

Schritte zur Lösung

\frac{12 x ^{3} - 37 x ^{2} + 48 x - 36}{( x - 2 ) ^{2} ( x ^{2} + 4 )}

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

= \frac{12 x ^{3} - 37 x ^{2} + 48 x - 36}{( x ^{2} - 4 x + 4 ) ( x ^{2} + 4 )}

Multipliziere aus

(x^{2} - 4 x + 4) (x^{2} + 4) : x^{4} + 8 x^{2} - 4 x^{3} - 16 x + 16

= \frac{12 x ^{3} - 37 x ^{2} + 48 x - 36}{x ^{4} + 8 x ^{2} - 4 x ^{3} - 16 x + 16}

s im pl i f y (x - 2 + 6) (x - 2 - 6)

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

e x p an d (1 - cos (a)) (1 + cos (a))

s im pl i f y (1 + 3 i)^{5}

e x p an d (x + \frac{1}{x})^{4}