erweitern (8(2x^2-8x-1))/(3x^{4/3)(x+1)^3}

Lösung

erweitern

\frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{4}{3}} ( x + 1 ) ^{3}}

\frac{16 x ^{2} - 64 x - 8}{3 x ^{\frac{13}{3}} + 9 x ^{\frac{10}{3}} + 9 x ^{\frac{7}{3}} + 3 x ^{\frac{4}{3}}}

Schritte zur Lösung

\frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{4}{3}} ( x + 1 ) ^{3}}

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

= \frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{4}{3}} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}

Multipliziere aus

3 x^{\frac{4}{3}} (x^{3} + 3 x^{2} + 3 x + 1) : 3 x^{\frac{13}{3}} + 9 x^{\frac{10}{3}} + 9 x^{\frac{7}{3}} + 3 x^{\frac{4}{3}}

= \frac{8 ( 2 x ^{2} - 8 x - 1 )}{3 x ^{\frac{13}{3}} + 9 x ^{\frac{10}{3}} + 9 x ^{\frac{7}{3}} + 3 x ^{\frac{4}{3}}}

Multipliziere aus

8 (2 x^{2} - 8 x - 1) : 16 x^{2} - 64 x - 8

= \frac{16 x ^{2} - 64 x - 8}{3 x ^{\frac{13}{3}} + 9 x ^{\frac{10}{3}} + 9 x ^{\frac{7}{3}} + 3 x ^{\frac{4}{3}}}

e x p an d 6 (3 x [- 5])

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

e x p an d - \frac{3 j x ( a e ^{\frac{π}{t}} - b e ^{\frac{π}{t}} )}{2}

s im pl i f y \frac{( ( a \cdot ( 1 + g ) ^{n} ) \cdot ( 1 - 0.6 a ) )}{c} - c

e x p an d \frac{5 x ^{4} - 3 x ^{2}}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}}