展开 1/((1-x)^3(1+x)(1-x^5))

解答

展开

\frac{1}{( 1 - x ) ^{3} ( 1 + x ) ( 1 - x ^{5} )}

\frac{1}{1 - x ^{5} - 2 x + 2 x ^{6} + 2 x ^{3} - 2 x ^{8} - x ^{4} + x ^{9}}

求解步骤

\frac{1}{( 1 - x ) ^{3} ( 1 + x ) ( 1 - x ^{5} )}

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

= \frac{1}{( - x ^{3} + 3 x ^{2} - 3 x + 1 ) ( x + 1 ) ( - x ^{5} + 1 )}

乘开

(1 - 3 x + 3 x^{2} - x^{3}) (1 + x) (1 - x^{5}) : 1 - x^{5} - 2 x + 2 x^{6} + 2 x^{3} - 2 x^{8} - x^{4} + x^{9}

= \frac{1}{1 - x ^{5} - 2 x + 2 x ^{6} + 2 x ^{3} - 2 x ^{8} - x ^{4} + x ^{9}}

e x p an d (2 x^{2} - \frac{1}{4 x})^{8}

e x p an d g^{'} (1) (- 3 z^{\frac{10}{9}} - 4 z^{\frac{11}{4}} + 8 z^{\frac{4}{3}})

s im pl i f y (- x - u)^{2}

e x p an d 2 (y + x = 6) 2 y + 2 x

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