erweitern ((x^2+x+5)(x^2-9))/((x+6)^4(x+2)^3)

Lösung

erweitern

\frac{( x ^{2} + x + 5 ) ( x ^{2} - 9 )}{( x + 6 ) ^{4} ( x + 2 ) ^{3}}

\frac{x ^{4} - 4 x ^{2} + x ^{3} - 9 x - 45}{x ^{7} + 30 x ^{6} + 372 x ^{5} + 2456 x ^{4} + 9264 x ^{3} + 19872 x ^{2} + 22464 x + 10368}

Schritte zur Lösung

\frac{( x ^{2} + x + 5 ) ( x ^{2} - 9 )}{( x + 6 ) ^{4} ( x + 2 ) ^{3}}

(x + 6)^{4} = x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296

= \frac{( x ^{2} + x + 5 ) ( x ^{2} - 9 )}{( x ^{4} + 24 x ^{3} + 216 x ^{2} + 864 x + 1296 ) ( x + 2 ) ^{3}}

(x + 2)^{3} = x^{3} + 6 x^{2} + 12 x + 8

= \frac{( x ^{2} + x + 5 ) ( x ^{2} - 9 )}{( x ^{4} + 24 x ^{3} + 216 x ^{2} + 864 x + 1296 ) ( x ^{3} + 6 x ^{2} + 12 x + 8 )}

Multipliziere aus

(x^{4} + 24 x^{3} + 216 x^{2} + 864 x + 1296) (x^{3} + 6 x^{2} + 12 x + 8) : x^{7} + 30 x^{6} + 372 x^{5} + 2456 x^{4} + 9264 x^{3} + 19872 x^{2} + 22464 x + 10368

= \frac{( x ^{2} + x + 5 ) ( x ^{2} - 9 )}{x ^{7} + 30 x ^{6} + 372 x ^{5} + 2456 x ^{4} + 9264 x ^{3} + 19872 x ^{2} + 22464 x + 10368}

Multipliziere aus

(x^{2} + x + 5) (x^{2} - 9) : x^{4} - 4 x^{2} + x^{3} - 9 x - 45

= \frac{x ^{4} - 4 x ^{2} + x ^{3} - 9 x - 45}{x ^{7} + 30 x ^{6} + 372 x ^{5} + 2456 x ^{4} + 9264 x ^{3} + 19872 x ^{2} + 22464 x + 10368}

s im pl i f y (4 + 3 i)^{4}

e x p an d (x + i y)^{5}

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

e x p an d (x - 5) (x^{2} - 9 + 4)

e x p an d e^{x} (sin (y) + 3 y) d x - (3 x - e^{x} (sin (y)) d y = 0)