erweitern (3(c-x^3)^2+3c+6x^3)/((c-x^3)^2)

Lösung

erweitern

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

\frac{3 c ^{2} - 6 c x ^{3} + 3 x ^{6} + 3 c + 6 x ^{3}}{c ^{2} - 2 c x ^{3} + x ^{6}}

Schritte zur Lösung

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

(c - x^{3})^{2} = c^{2} - 2 c x^{3} + x^{6}

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

(c - x^{3})^{2} = c^{2} - 2 c x^{3} + x^{6}

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

Multipliziere aus

3 (c^{2} - 2 c x^{3} + x^{6}) + 3 c + 6 x^{3} : 3 c^{2} - 6 c x^{3} + 3 x^{6} + 3 c + 6 x^{3}

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

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

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

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

e x p an d \frac{k ( s - 1 )}{( s + 2 ) ( s + 4 )}

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