erweitern (5x^2+12x+3)/(x(x+1)^2)

Lösung

erweitern

\frac{5 x ^{2} + 12 x + 3}{x ( x + 1 ) ^{2}}

\frac{5 x ^{2} + 12 x + 3}{x ^{3} + 2 x ^{2} + x}

Schritte zur Lösung

\frac{5 x ^{2} + 12 x + 3}{x ( x + 1 ) ^{2}}

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

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

Multipliziere aus

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

= \frac{5 x ^{2} + 12 x + 3}{x ^{3} + 2 x ^{2} + x}

e x p an d 3 (x + 3) (\frac{10}{x + 3} + \frac{10}{3} = 6)

e x p an d \frac{r ( 2 + r )}{2}

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

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

s im pl i f y (1 + i)^{19}