erweitern (x^2+5x+7)/((x^2+4x+5)(s+1)^2)

Lösung

erweitern

\frac{x ^{2} + 5 x + 7}{( x ^{2} + 4 x + 5 ) ( s + 1 ) ^{2}}

\frac{x ^{2} + 5 x + 7}{x ^{2} s ^{2} + 2 x ^{2} s + x ^{2} + 4 x s ^{2} + 8 x s + 4 x + 5 s ^{2} + 10 s + 5}

Schritte zur Lösung

\frac{x ^{2} + 5 x + 7}{( x ^{2} + 4 x + 5 ) ( s + 1 ) ^{2}}

(s + 1)^{2} = s^{2} + 2 s + 1

= \frac{x ^{2} + 5 x + 7}{( x ^{2} + 4 x + 5 ) ( s ^{2} + 2 s + 1 )}

Multipliziere aus

(x^{2} + 4 x + 5) (s^{2} + 2 s + 1) : x^{2} s^{2} + 2 x^{2} s + x^{2} + 4 x s^{2} + 8 x s + 4 x + 5 s^{2} + 10 s + 5

= \frac{x ^{2} + 5 x + 7}{x ^{2} s ^{2} + 2 x ^{2} s + x ^{2} + 4 x s ^{2} + 8 x s + 4 x + 5 s ^{2} + 10 s + 5}

e x p an d, (8 x^{2} - 8) + (- 2 x^{2} - 9 x)

e x p an d \frac{( sin ^{2} ( t ) )}{( 1 - cos ( t ) ) ^{2}}

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

e x p an d (x + 1) (x - x)

s im pl i f y 3 (2 + 3)