erweitern-(3(4x^3+6x^2h+4xh^2+h^3))/(x^4(x+h)^4)

Lösung

erweitern

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

- \frac{12 x ^{3} + 18 x ^{2} h + 12 x h ^{2} + 3 h ^{3}}{x ^{8} + 4 x ^{7} h + 6 x ^{6} h ^{2} + 4 x ^{5} h ^{3} + x ^{4} h ^{4}}

Schritte zur Lösung

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

(x + h)^{4} = x^{4} + 4 x^{3} h + 6 x^{2} h^{2} + 4 x h^{3} + h^{4}

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

Multipliziere aus

x^{4} (x^{4} + 4 x^{3} h + 6 x^{2} h^{2} + 4 x h^{3} + h^{4}) : x^{8} + 4 x^{7} h + 6 x^{6} h^{2} + 4 x^{5} h^{3} + x^{4} h^{4}

= - \frac{3 ( 4 x ^{3} + 6 x ^{2} h + 4 x h ^{2} + h ^{3} )}{x ^{8} + 4 x ^{7} h + 6 x ^{6} h ^{2} + 4 x ^{5} h ^{3} + x ^{4} h ^{4}}

Multipliziere aus

3 (4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3}) : 12 x^{3} + 18 x^{2} h + 12 x h^{2} + 3 h^{3}

= - \frac{12 x ^{3} + 18 x ^{2} h + 12 x h ^{2} + 3 h ^{3}}{x ^{8} + 4 x ^{7} h + 6 x ^{6} h ^{2} + 4 x ^{5} h ^{3} + x ^{4} h ^{4}}

e x p an d \frac{1}{( a - 2 x ) ^{2} ( b - x )}

e x p an d \frac{12 x}{( x ^{2} + 6 ) ^{2}}

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

s im pl i f y (3 + 1 - y^{2})^{2}

s im pl i f y (3 y^{4} + \frac{2 n}{7}) \cdot (3 y^{4} - 2 x^{2})