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

Lösung

erweitern

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

\frac{3 x ^{3} + 9 x ^{2} - x ^{4} - 2 x}{x ^{2} + 6 x + 9}

Schritte zur Lösung

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

(x + 3)^{2} = x^{2} + 6 x + 9

= \frac{3 x ^{2} ( x + 3 ) - x ( x ^{3} + 2 )}{x ^{2} + 6 x + 9}

Multipliziere aus

3 x^{2} (x + 3) - x (x^{3} + 2) : 3 x^{3} + 9 x^{2} - x^{4} - 2 x

= \frac{3 x ^{3} + 9 x ^{2} - x ^{4} - 2 x}{x ^{2} + 6 x + 9}

e x p an d D x [(1 + x^{2}) (1 + 2 x^{2})]

s im pl i f y x (800 - \frac{x}{6})

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

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

e x p an d - \frac{2 s + 9}{( s + 5 ) ( s + 2 )}