erweitern (x^2+3x+15)/((x+3)^2(x^2+7))

Lösung

erweitern

\frac{x ^{2} + 3 x + 15}{( x + 3 ) ^{2} ( x ^{2} + 7 )}

\frac{x ^{2} + 3 x + 15}{x ^{4} + 16 x ^{2} + 6 x ^{3} + 42 x + 63}

Schritte zur Lösung

\frac{x ^{2} + 3 x + 15}{( x + 3 ) ^{2} ( x ^{2} + 7 )}

(x + 3)^{2} = x^{2} + 6 x + 9

= \frac{x ^{2} + 3 x + 15}{( x ^{2} + 6 x + 9 ) ( x ^{2} + 7 )}

Multipliziere aus

(x^{2} + 6 x + 9) (x^{2} + 7) : x^{4} + 16 x^{2} + 6 x^{3} + 42 x + 63

= \frac{x ^{2} + 3 x + 15}{x ^{4} + 16 x ^{2} + 6 x ^{3} + 42 x + 63}

e x p an d \frac{1}{25} (e^{5 t} \cdot 5 t - e^{- 5 t})

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

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

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

e x p an d - \frac{k + 1}{k ( k - 1 )}