erweitern ((x+1)^2(x-3))/((x-4)^3(x+5))

Lösung

erweitern

\frac{( x + 1 ) ^{2} ( x - 3 )}{( x - 4 ) ^{3} ( x + 5 )}

\frac{x ^{3} - x ^{2} - 5 x - 3}{x ^{4} - 7 x ^{3} - 12 x ^{2} + 176 x - 320}

Schritte zur Lösung

\frac{( x + 1 ) ^{2} ( x - 3 )}{( x - 4 ) ^{3} ( x + 5 )}

(x - 4)^{3} = x^{3} - 12 x^{2} + 48 x - 64

= \frac{( x + 1 ) ^{2} ( x - 3 )}{( x ^{3} - 12 x ^{2} + 48 x - 64 ) ( x + 5 )}

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

= \frac{( x ^{2} + 2 x + 1 ) ( x - 3 )}{( x ^{3} - 12 x ^{2} + 48 x - 64 ) ( x + 5 )}

Multipliziere aus

(x^{3} - 12 x^{2} + 48 x - 64) (x + 5) : x^{4} - 7 x^{3} - 12 x^{2} + 176 x - 320

= \frac{( x ^{2} + 2 x + 1 ) ( x - 3 )}{x ^{4} - 7 x ^{3} - 12 x ^{2} + 176 x - 320}

Multipliziere aus

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

= \frac{x ^{3} - x ^{2} - 5 x - 3}{x ^{4} - 7 x ^{3} - 12 x ^{2} + 176 x - 320}

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

e x p an d \frac{- 2 x ^{2} + 10 x + 4}{( x - 1 ) ( x ^{2} + 2 x + 9 )}

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

e x p an d - e^{2 x} (2 e^{- 2 x} - e^{- x})

e x p an d \frac{( 45 a ^{2} - b )}{( 30 ab )}