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

Lösung

erweitern

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

\frac{- x ^{5} + 9 x ^{4} - 25 x ^{3} + 9 x ^{2} + 54 x - 54}{x ^{3} - 2 x ^{2} - 7 x - 4}

Schritte zur Lösung

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

(x - 3)^{3} = x^{3} - 9 x^{2} + 27 x - 27

= \frac{( - x ^{2} + 2 ) ( x ^{3} - 9 x ^{2} + 27 x - 27 )}{( x + 1 ) ( x ^{2} - 3 x - 4 )}

Multipliziere aus

(x + 1) (x^{2} - 3 x - 4) : x^{3} - 2 x^{2} - 7 x - 4

= \frac{( - x ^{2} + 2 ) ( x ^{3} - 9 x ^{2} + 27 x - 27 )}{x ^{3} - 2 x ^{2} - 7 x - 4}

Multipliziere aus

(2 - x^{2}) (x^{3} - 9 x^{2} + 27 x - 27) : - x^{5} + 9 x^{4} - 25 x^{3} + 9 x^{2} + 54 x - 54

= \frac{- x ^{5} + 9 x ^{4} - 25 x ^{3} + 9 x ^{2} + 54 x - 54}{x ^{3} - 2 x ^{2} - 7 x - 4}

e x p an d (3 x^{2} + y^{2}) d x - (a x^{2} + 2 b x y) d y

e x p an d x^{2} (e^{3 s} - 1)

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

e x p an d \frac{12 x + 7}{4} - \frac{30 - 18 x}{6}

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