erweitern (x^2-5x+1)/((9+x^2)(x+2)(x-1)^2)

Lösung

erweitern

\frac{x ^{2} - 5 x + 1}{( 9 + x ^{2} ) ( x + 2 ) ( x - 1 ) ^{2}}

\frac{x ^{2} - 5 x + 1}{x ^{5} + 6 x ^{3} + 2 x ^{2} - 27 x + 18}

Schritte zur Lösung

\frac{x ^{2} - 5 x + 1}{( 9 + x ^{2} ) ( x + 2 ) ( x - 1 ) ^{2}}

(x - 1)^{2} = x^{2} - 2 x + 1

= \frac{x ^{2} - 5 x + 1}{( x ^{2} + 9 ) ( x + 2 ) ( x ^{2} - 2 x + 1 )}

Multipliziere aus

(9 + x^{2}) (x + 2) (x^{2} - 2 x + 1) : x^{5} + 6 x^{3} + 2 x^{2} - 27 x + 18

= \frac{x ^{2} - 5 x + 1}{x ^{5} + 6 x ^{3} + 2 x ^{2} - 27 x + 18}

e x p an d 33 (2 - 23)

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

s im pl i f y (x^{\frac{1}{2}}) (6 x^{5} + 15 x^{4} + 12 x^{3} + 9 x^{2})

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

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