erweitern (x^2+5)/((x-1)(x^2+4)^2)

Lösung

erweitern

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

\frac{x ^{2} + 5}{x ^{5} + 8 x ^{3} + 16 x - x ^{4} - 8 x ^{2} - 16}

Schritte zur Lösung

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

(x^{2} + 4)^{2} = x^{4} + 8 x^{2} + 16

= \frac{x ^{2} + 5}{( x - 1 ) ( x ^{4} + 8 x ^{2} + 16 )}

Multipliziere aus

(x - 1) (x^{4} + 8 x^{2} + 16) : x^{5} + 8 x^{3} + 16 x - x^{4} - 8 x^{2} - 16

= \frac{x ^{2} + 5}{x ^{5} + 8 x ^{3} + 16 x - x ^{4} - 8 x ^{2} - 16}

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

e x p an d \frac{x ^{2} ( x + 1 ) ^{3}}{( x - 2 ) ^{2} ( x - 4 ) ^{4}}

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

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

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