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

Lösung

erweitern

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

\frac{x}{x ^{19} + 36 x ^{17} + 576 x ^{15} + 5376 x ^{13} + 32256 x ^{11} + 129024 x ^{9} + 344064 x ^{7} + 589824 x ^{5} + 589824 x ^{3} + 262144 x - 3 x ^{18} - 108 x ^{16} - 1728 x ^{14} - 16128 x ^{12} - 96768 x ^{10} - 387072 x ^{8} - 1032192 x ^{6} - 1769472 x ^{4} - 1769472 x ^{2} - 786432}

Schritte zur Lösung

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

(x^{2} + 4)^{9} = x^{18} + 36 x^{16} + 576 x^{14} + 5376 x^{12} + 32256 x^{10} + 129024 x^{8} + 344064 x^{6} + 589824 x^{4} + 589824 x^{2} + 262144

= \frac{x}{( x - 3 ) ( x ^{18} + 36 x ^{16} + 576 x ^{14} + 5376 x ^{12} + 32256 x ^{10} + 129024 x ^{8} + 344064 x ^{6} + 589824 x ^{4} + 589824 x ^{2} + 262144 )}

Multipliziere aus

(x - 3) (x^{18} + 36 x^{16} + 576 x^{14} + 5376 x^{12} + 32256 x^{10} + 129024 x^{8} + 344064 x^{6} + 589824 x^{4} + 589824 x^{2} + 262144) : x^{19} + 36 x^{17} + 576 x^{15} + 5376 x^{13} + 32256 x^{11} + 129024 x^{9} + 344064 x^{7} + 589824 x^{5} + 589824 x^{3} + 262144 x - 3 x^{18} - 108 x^{16} - 1728 x^{14} - 16128 x^{12} - 96768 x^{10} - 387072 x^{8} - 1032192 x^{6} - 1769472 x^{4} - 1769472 x^{2} - 786432

= \frac{x}{x ^{19} + 36 x ^{17} + 576 x ^{15} + 5376 x ^{13} + 32256 x ^{11} + 129024 x ^{9} + 344064 x ^{7} + 589824 x ^{5} + 589824 x ^{3} + 262144 x - 3 x ^{18} - 108 x ^{16} - 1728 x ^{14} - 16128 x ^{12} - 96768 x ^{10} - 387072 x ^{8} - 1032192 x ^{6} - 1769472 x ^{4} - 1769472 x ^{2} - 786432}

e x p an d \frac{1}{s ( b s + 1 )}

e x p an d (- 20 x + 4 y = 12) 9

e x p an d (3 y d x + 6 d x - x d y = 0) \frac{d y}{x d x}

e x p an d 2 (x + 1) (ln (x + 1)) + x + 1

\frac{d}{d θ} ((x) (c + v (x, θ) cos (θ)))