erweitern (3x^2-4x+7)/((x+1)^3(x^2+1)^2(x-7))

Lösung

erweitern

\frac{3 x ^{2} - 4 x + 7}{( x + 1 ) ^{3} ( x ^{2} + 1 ) ^{2} ( x - 7 )}

\frac{3 x ^{2} - 4 x + 7}{x ^{8} - 4 x ^{7} - 16 x ^{6} - 28 x ^{5} - 42 x ^{4} - 44 x ^{3} - 32 x ^{2} - 20 x - 7}

Schritte zur Lösung

\frac{3 x ^{2} - 4 x + 7}{( x + 1 ) ^{3} ( x ^{2} + 1 ) ^{2} ( x - 7 )}

(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1

= \frac{3 x ^{2} - 4 x + 7}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x ^{2} + 1 ) ^{2} ( x - 7 )}

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

= \frac{3 x ^{2} - 4 x + 7}{( x ^{3} + 3 x ^{2} + 3 x + 1 ) ( x ^{4} + 2 x ^{2} + 1 ) ( x - 7 )}

Multipliziere aus

(x^{3} + 3 x^{2} + 3 x + 1) (x^{4} + 2 x^{2} + 1) (x - 7) : x^{8} - 4 x^{7} - 16 x^{6} - 28 x^{5} - 42 x^{4} - 44 x^{3} - 32 x^{2} - 20 x - 7

= \frac{3 x ^{2} - 4 x + 7}{x ^{8} - 4 x ^{7} - 16 x ^{6} - 28 x ^{5} - 42 x ^{4} - 44 x ^{3} - 32 x ^{2} - 20 x - 7}

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

e x p an d (2 x + 6) sin (x)

s im pl i f y (a + b) (a - b)

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

s im pl i f y (2 x + 5)^{2}