erweitern ((5s^3-56s^2+46s-534))/((s^2+9)(s-6)^2)

Lösung

erweitern

\frac{( 5 s ^{3} - 56 s ^{2} + 46 s - 534 )}{( s ^{2} + 9 ) ( s - 6 ) ^{2}}

\frac{5 s ^{3} - 56 s ^{2} + 46 s - 534}{s ^{4} - 12 s ^{3} + 45 s ^{2} - 108 s + 324}

Schritte zur Lösung

\frac{5 s ^{3} - 56 s ^{2} + 46 s - 534}{( s ^{2} + 9 ) ( s - 6 ) ^{2}}

(s - 6)^{2} = s^{2} - 12 s + 36

= \frac{5 s ^{3} - 56 s ^{2} + 46 s - 534}{( s ^{2} + 9 ) ( s ^{2} - 12 s + 36 )}

Multipliziere aus

(s^{2} + 9) (s^{2} - 12 s + 36) : s^{4} - 12 s^{3} + 45 s^{2} - 108 s + 324

= \frac{5 s ^{3} - 56 s ^{2} + 46 s - 534}{s ^{4} - 12 s ^{3} + 45 s ^{2} - 108 s + 324}

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

e x p an d \frac{18 s ^{2} + 131 s + 439}{( s + 4 ) ( s ^{2} + 4 s + 29 )}

e x p an d (5 + \frac{4}{x ^{3}}) (2 x + \frac{3}{x ^{2}})^{15}

e x p an d (- 3, - 11) v er t e x (0, - 2)

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