erweitern (x^2+2x+3)/((x-1)^2(x-2)(x^2+4))

Lösung

erweitern

\frac{x ^{2} + 2 x + 3}{( x - 1 ) ^{2} ( x - 2 ) ( x ^{2} + 4 )}

\frac{x ^{2} + 2 x + 3}{x ^{5} - 4 x ^{4} + 9 x ^{3} - 18 x ^{2} + 20 x - 8}

Schritte zur Lösung

\frac{x ^{2} + 2 x + 3}{( x - 1 ) ^{2} ( x - 2 ) ( x ^{2} + 4 )}

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

= \frac{x ^{2} + 2 x + 3}{( x ^{2} - 2 x + 1 ) ( x - 2 ) ( x ^{2} + 4 )}

Multipliziere aus

(x^{2} - 2 x + 1) (x - 2) (x^{2} + 4) : x^{5} - 4 x^{4} + 9 x^{3} - 18 x^{2} + 20 x - 8

= \frac{x ^{2} + 2 x + 3}{x ^{5} - 4 x ^{4} + 9 x ^{3} - 18 x ^{2} + 20 x - 8}

e x p an d - \frac{2 ( 4 + 6 )}{5}

e x p an d e^{t} θ (t - 2)

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

e x p an d \frac{7}{( 2 + j ) ^{2}}

e x p an d \frac{12 s ^{2}}{( 3 s + 1 ) ^{2}}