erweitern (19(40s+11))/(6(4s+3)^2(5s-1)^2)

Lösung

erweitern

\frac{19 ( 40 s + 11 )}{6 ( 4 s + 3 ) ^{2} ( 5 s - 1 ) ^{2}}

\frac{760 s + 209}{2400 s ^{4} + 2640 s ^{3} + 6 s ^{2} - 396 s + 54}

Schritte zur Lösung

\frac{19 ( 40 s + 11 )}{6 ( 4 s + 3 ) ^{2} ( 5 s - 1 ) ^{2}}

(4 s + 3)^{2} = 16 s^{2} + 24 s + 9

= \frac{19 ( 40 s + 11 )}{6 ( 16 s ^{2} + 24 s + 9 ) ( 5 s - 1 ) ^{2}}

(5 s - 1)^{2} = 25 s^{2} - 10 s + 1

= \frac{19 ( 40 s + 11 )}{6 ( 16 s ^{2} + 24 s + 9 ) ( 25 s ^{2} - 10 s + 1 )}

Multipliziere aus

6 (16 s^{2} + 24 s + 9) (25 s^{2} - 10 s + 1) : 2400 s^{4} + 2640 s^{3} + 6 s^{2} - 396 s + 54

= \frac{19 ( 40 s + 11 )}{2400 s ^{4} + 2640 s ^{3} + 6 s ^{2} - 396 s + 54}

Multipliziere aus

19 (40 s + 11) : 760 s + 209

= \frac{760 s + 209}{2400 s ^{4} + 2640 s ^{3} + 6 s ^{2} - 396 s + 54}

e x p an d 6 (3 x - 10 = 5 (2 x + 15))

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

e x p an d \frac{( n + 1 ) ( n + 2 ) ( 2 n + 9 )}{6}

e x p an d \frac{2}{x ( x ^{2} - 16 )}

f (x) = \frac{2 x ^{5} + 28 x ^{3} - 6 x}{( x ^{2} - 1 ) ^{4}}