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

Lösung

erweitern

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

\frac{- 4 x ^{3} + 1}{2 x ^{\frac{13}{2}} + 4 x ^{\frac{7}{2}} + 2 x ^{\frac{1}{2}}}

Schritte zur Lösung

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

(x^{3} + 1)^{2} = x^{6} + 2 x^{3} + 1

= \frac{- 4 x ^{3} + 1}{2 x ^{\frac{1}{2}} ( x ^{6} + 2 x ^{3} + 1 )}

Multipliziere aus

2 x^{\frac{1}{2}} (x^{6} + 2 x^{3} + 1) : 2 x^{\frac{13}{2}} + 4 x^{\frac{7}{2}} + 2 x^{\frac{1}{2}}

= \frac{- 4 x ^{3} + 1}{2 x ^{\frac{13}{2}} + 4 x ^{\frac{7}{2}} + 2 x ^{\frac{1}{2}}}

e x p an d (2 x^{3} + 9 x^{2} + 3 x - 4) d i v i d e (x + 4)

\frac{d}{d x} ((f (x, y)) f (x, y) (x^{3} - 3 x y + y^{2}))

\frac{\partial}{\partial t} ((x) (x^{2} + y^{2}))

e x p an d \frac{K}{x ( 1 - x T )}

e x p an d (x^{2} + 1) y^{'} (x) + x y - 2 x