erweitern (4-9x-5x^2)/((x^2+4)(x-1)^2)

Lösung

erweitern

\frac{4 - 9 x - 5 x ^{2}}{( x ^{2} + 4 ) ( x - 1 ) ^{2}}

\frac{4 - 9 x - 5 x ^{2}}{x ^{4} - 2 x ^{3} + 5 x ^{2} - 8 x + 4}

Schritte zur Lösung

\frac{4 - 9 x - 5 x ^{2}}{( x ^{2} + 4 ) ( x - 1 ) ^{2}}

(x - 1)^{2} = x^{2} - 2 x + 1

= \frac{4 - 9 x - 5 x ^{2}}{( x ^{2} + 4 ) ( x ^{2} - 2 x + 1 )}

Multipliziere aus

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

= \frac{4 - 9 x - 5 x ^{2}}{x ^{4} - 2 x ^{3} + 5 x ^{2} - 8 x + 4}

e x p an d 4 (3 + \frac{1}{4} c - \frac{1}{2} d)

e x p an d (x - 2) l e f t (x + 2)

e x p an d (x - \frac{π}{3})^{2}

e x p an d \frac{4 e ^{2 x}}{( e ^{2 x} + 1 ) ^{2}}

e x p an d (e^{x}) (x e^{- x} - e^{- x})